Write an equation for an exponential growth function y=f(x) where the initial population is 6000...
Question:
Write an equation for an exponential growth function {eq}y=f(x) {/eq} where the initial population is 6000 and the growth factor is 1.132.
Exponential Functions:
There are many types of exponential functions. Where the base of the exponent of the function is not the mathematical constant {eq}e {/eq}, the base is the constant that represents the growth factor.
Answer and Explanation:
Become a Study.com member to unlock this answer! Create your account
View this answerSee full answer below.
Ask a question
Our experts can answer your tough homework and study questions.
Ask a question Ask a questionSearch Answers
Learn more about this topic:

Get access to this video and our entire Q&A library
What Is an Exponential Function?
from
Chapter 10 / Lesson 1
143K
How does the exponential function equation work? Learn the parts of an exponential function and what makes a function exponential with graphs and examples.
Related to this Question
- Write an equation for an exponential growth function y = f(x) where the initial population is 3000 and the growth factor is 1.085.
- Identify the initial amount a and the growth factor b in the exponential function { g(x)=4x^2. }
- Identify the initial amount and the growth factor b in the exponential function. y= 5(0.5)^x
- Identify the initial amount a and the growth factor b in the exponential function g(x) = 14 ast 2^x a. a = 14, b = x b. a = 14, b = 2 c. a = 28, b = 1 d. a = 28, b = x
- Find a linear equation in the form P = m t + b , which gives the population, p , and t years from 2010. This is based from an initial population of 6,000 in 2010, with a growth of 200 ppl per year
- Assume an exponential function has a starting value of 13 and a growth rate of 0.35%. Write an equation to model the situation.
- Suppose a population of bacteria is changing at a rate of \frac{dp}{dt} = \frac{1.000}{1 + 0.5 t}, where t is the time in days. The initial population (when t = 0) is 500. Write an equation that gives
- Suppose that a population has a carrying capacity, K=60 , and unrestricted growth rate, r_\mathrm{ max}=0.02. Let the initial condition be p_0 = 10. Write the logistic difference equation for the population and calculate p_2 .
- A population grows according to an exponential growth model, with P0 = 8 and P1 = 152. a) Complete the recursive formula: Pn = x Pn-1. b) Write an explicit formula for Pn. Pn =
- Determine if the equation { y = 2^x } represents exponential growth or decay?
- In 1998, the population of a given country was 37 million, and the exponential growth rate was 5% per year. Find the exponential growth function.
- The equation y = 400(1.03)^{x} is an example of what? A. Exponential growth B. Exponential decay C. Not exponential
- Identify the initial amount a and the growth factor b in the exponential function. f(t)=1.4^t a. a=1, b=0.4 b. a=1.4, b=0 c. a=1.4, b=t a. a=1, b=1.4
- (a) Write the solution of the initial-value problem and use it to find the population when t = 20. (b) When does the population reach 1200?
- Find the point at which the rate of population growth begins to slow down under the logistic equation.
- A population of bears increased by 50% in 4 years. If the situation is modeled by an annual growth rate compounded continuously, what formula could be used to find the annual rate according to the exponential growth function? Give your answer in terms of
- Given the logistic growth model \frac{dP}{dt} = 0.02P(400 - P), with P(0) = 200. a) Write the solution to this initial-value problem. (b) At what time does the population P reach 300?
- The following function represents exponential growth or decay. P = 2.6e^{0.09t} a) What is the initial quantity? b) What is the growth rate? State if the growth rate is continuous.
- The function P(t) = 1.5e^{0.3t} represents exponential growth or decay. a. What is the initial quantity? b. What is the continuous growth rate ?
- The following function represents exponential growth or decay. P = 2.6 e^{0.09t} What is the initial quantity? What is the growth rate? State if the growth rate is continuous.
- (a) Write a differential equation that expresses the law of natural growth. (b) Under what circumstances is this an appropriate model for population growth? (c) What are the solutions of this equation?
- Suppose that a population, whose size at time N(t), grows according to \frac{dN}{dt} = \frac{1}{100}N^2, with N(0) = 10. A. Solve for N(t). B. Graph N(t) as a function of t for 0 less than or equal to
- How do you determine if the equation y = 0.5(1.2)^x represents exponential growth or decay?
- How do you determine if the equation y = (0.3)^x represents exponential growth or decay?
- How do you determine if the equation y = 0.25(1.03)^5 represents exponential growth or decay?
- Write an exponential function to model the situation. Then predict the value of the function after 5 years (to the nearest whole number). A population of 210 animals that increases at an annual rate o
- Decide whether the function is an exponential growth or exponential decay function, and find the constant percentage rate of growth or decay. f(x) = 2500 \cdot 0.9968^{x}
- Consider the population function P(t) = 800/(1+7e^{-0.2t}), what is the instantaneous growth rate at t=5?
- Find a logistic function that describes the given population. Then graph the population function. The population increases from 500 to 800 in the first year and eventually levels off at 4,500. Write the equation of a logic function that models the given
- Given that a quantity Q(t) is described by the exponential growth function Q(t) = 590e^{0.02t} Q(t) = 590e^{0.02t}
- A population of bacteria P is changing at a rate based on the function given below, where t is time in days. The initial population (when t = 0) is 1100. \frac{dP}{dt}=\frac{3100}{1+0.25t} Write an eq
- A population of bacteria is changing at a rate of \frac{dP}{dt} =\frac{3000}{1+0.25t} where t is the time (in days). The initial population (when t = 0) is 1000. Write an equation that gives the population at any time t, and find the population when t = 3
- Suppose that a certain population obeys the logistic equation dy/dt = ry (1 y/K). a. If y_0 = K/8, find the time tau at which the initial population has doubled. Find the value of tau corresponding to r = 0.025 per year. (Enter an exact answer.) b. If y
- Suppose the size of a population at time t is N(t), and the growth rate of the population is given by the logistic growth function \frac{dN}{dt} = rN (1-\frac{N}{K}), t\geq 0 where r and K are positiv
- The population P of a community t years since it is established is modelled by P = 2100.(1.025)^t. Find a and k if the exponential function given is written in the form P = ae^{kt}.
- A population of bacteria is initially 2,000. After three hours the population is 1,000. Assuming this rate of decay continues, find the exponential function that represents the size of the bacteria population after t hours. Write your answer in the form
- Suppose that a certain population obeys the logistic equation d y d t = r y [ 1 - ( y / K ) ] with y ( 0 ) = y 0 . (Here, y ( t ) is the population at time t ). (a) If y 0 = K/ 6 , find the time T at which the initial population has doubled.
- Write a differential equation that expresses the law of natural growth. What does it say in terms of relative growth rate?
- Suppose a population grows according to a logistic model with initial population 100 and carrying capacity 1,000. If the population grows to 250 after one year, what will the population be after anoth
- Suppose a population grows according to a logistic model with initial population 200 and carrying capacity 2,000. If the population grows to 500 after one year, what will the population be after anoth
- Suppose a population grows according to a logistic model with initial population 1000 and carrying capacity 10,000.If the population grows to 2500 after one year,What will the population be after anot
- Assume the population was 724 when t=0, and 4 years later it became 2334. Write a formula for the size of the population in t years: Population =..................... What is the population when t=12
- An exponential function f has a 3-unit growth factor of 1.61. What is the 1-unit growth factor for f?
- |x| 0| 1| 2| 3 |F(x)| 90| 117| 152.1| 197.73 a) Is the function linear or exponential? b) If linear, what is the rate of change? c) If exponential, what is the growth/decay factor? d) Write the equation for F(x).
- Solve the problem The logistic differential equation a. \frac{dP}{dt}=0.07P(700-P) describes the growth of a population P, where t is measured in years. Find the limiting population. answer: a.1400,
- The exponential function gives the approximate U.S. population, in millions, d decades after 1790. (The formula is valid only up to 1860.)(a) What is the yearly growth factor? (Round your answer to two decimal places.) Find a formula that gives the popul
- The population of a country dropped from 52.1 million in 1995 to 45.9 million is 2007. Assume that P(t), the population, in millions, t years after 1995, is decreasing according to the exponential decay model. a. Find the value of k and write an equation,
- Suppose we follow a population that grow, according to the logistic equation and find that N(0) = 10, N(5) = 22, N(100) = 30, N(200) = 30. Estimate r.
- The following functions represent exponential growth or decay. P = 6.2(0.82)^t a) What is the initial quantity? b) What is the growth rate? State if the growth is continuous.
- Suppose that a population develops according to the logistic equation
- An initial population of 298 quails increases at an annual rate of 8%. Write an exponential function to model the quail population. What will the approximate population be after 3 years?
- A population of lemmings grows at a rate proportional to the amount of the population present. Suppose the rate is 4.77% and the initial population is 142. A) Write the IVP (differential equation with initial conditions) for the population. B) Solve the
- A population of 15,000 small deer in a specific region has grown exponentially to 17,000 in 4 years. Write an exponential equation to express the population growth y in terms of time t in years.
- A population is modeled by the logistic differential equation dp/dt = kP (1-P/M) where P(t) is the population at time t, the carrying capacity is 10,000, and the initial population is 1,000. (a) Find the relative growth rate k, if P(1) = 2.500. (b) Wri
- Suppose a population grows according to a logistic model with an initial population 500 and carrying capacity 5,000. If the population grows to 1250 after one year, what will the population be after another three years?
- The exponential function N = 3.93 \times 1.34^d give the approximate U.S. population, in millions, d decades after 1790. (The formula is valid only up to 1860.) (a) What is the yearly growth factor? (Round your answer to two decimal places.)
- The logistic differential equation d P/ d t = 0.08 P ( 300 - P ) describes the growth of a population P , where t is measured in years. Find the limiting population. a. 300 b. 600 c. 150 d. 2
- Given the logistic differential equation, identify k and L. What will the population be when the rate of growth is maximized? dP / dt = 0.1 P - 0.0004 P^2.
- How do you determine whether the following function represents exponential growth or decay: y=3(5/2)^x
- Write an equation that represents a population of 370 animals that increases at an annual rate of 11%.
- How do you determine the multiplier for exponential growth and decay?
- The population of Collin County, which follows the exponential growth model, increased from 491,675 in 2000 to 782,341 in 2010 a. Find the exponential growth rate, k. Round the answer to four decimal places. b. write the exponential growth function. Use
- What is the exponential growth or decay of this function and the constant percentage 20(.876)^x
- The population of Murrayville doubled in 30 years. What was the exponential growth rate?
- Population of Murrayville doubled in 30 years. What was the exponential growth rate?
- An initial population of 745 quail increases at an annual rate of 16 percentage. Write an exponential function to model the quail population. What will the approximate population be after 4 years?
- Determine the rate at which the population grows each year Year -T Population=N Rate of Growth =Gr \\ 2016 872,406 \\ 2017 877460 \\ 2018 883490 \\ 2019 889,995 \\ 2020 896,444
- Suppose a population is dying with a half-life of 53 years. The initial size is 1900. Find the equation for population size P(t) as a function of time. (Round a to four decimal places.) P(t) =
- The size of a population p as a function of time t is given by dp/dt = 0.02p + 11t. Solve for p as a function of t if the initial population is 10,000.
- Suppose population grows according to the logistic equation \frac{\mathrm{d} P}{\mathrm{d} t}= 0.1P - 0.00002P^2 with P(0)= 300. (a) Calculate the relative growth rate and Carrying capacity. (b) Find
- An initial population P, of 1500 bacteria grows in number according to the equation p(t) = 1500( 1+ 5t/t^2 + 30) where t is in hours. Determine the rate at which the population is growing after 3 h. a. 0.069 bacteria/h b. 104 bacteria/h c. 281 bacteria/h
- a) Suppose Ted starts with 24 rabbits. Each year they grow to 10 times as many. Write an exponential function to represent the rabbit population, y, based on the number of years that passed, x. Describe what the variables represent and how the equation bu
- A population is modeled by the following function P(t) = 10/1+2e-0.05t, where t is time in years and P in millions. a. What was the initial population at time t = 0? b. Find the rate of change in the population at t = 50 years. c. What happens to the popu
- A population of lemmings grows at a rate proportional to the amount of the population present. Suppose the rate is 4.77% and the initial population is 142. (A) write the differential equation with initial conditions for the population. (B) Solve the IVP
- The size of a population p as a function of time t is given by \frac{dp}{dt}= 0.02p + 11t. Solve for p as a function of t if the initial population is 10,000.
- Suppose an initial population of 33 million people increases at a continuous percent rate of 1.8% per year since the beginning of 2000. Write a function f that determines the population (in millions) in terms of the number of years t since the beginning o
- \frac{dP}{dt} = 0.1P \left(1-\frac{P}{2000}\right) P(0) = 100 a) Write the solution of the initial-value problem and use it to find the population when t = 20. b) When does the population reach 1200?
- Given the exponential function, f(x) = 2(1.5)^{x}, answer the following: a.) State whether the function is a growth or decay function. b.) Identify the initial value. c.) Identify the growth/decay factor. d.) Identify the growth/decay rate.
- Make an exponential model y(t) with the given properties. Assume that t is the number of periods. The initial value is 65, and there is a 30% growth rate per period.
- A colony of bacteria doubles in population every 30 minutes starting from an initial population size of y_o. Let y(t) denote the population at time t. (a) Express y as an exponential function with base 2. (b) Express y as an exponential function with ba
- The population of Canada is 35 million and it increases each year by 1.2%. Write down an equation for the population t years from now and use logarithms to determine when the population will reach 50
- Explain the mathematical model for the exponential growth or decay.
- A population grows according to the following logistic model (where t is measured in years): P(t) = \dfrac{10,000}{1 + 1000e^{0.2t. What is the initial population size?
- The population of a county is growing at a rate of 9% per year, compounded continuously. How many years will it take for the population to quadruple according to the exponential growth function?
- A population numbers 10,000 organisms initially and grows by 9% each year. Suppose P represents population, and t the number of years of growth. Write an exponential model for the population in the form P = a \cdot b^t
- The rate of growth of a microbe population is given by m'(t) = 30t e^2t, where t is time in days. What is the total accumulated growth during the first 2 days?
- The rate of growth of a microbe population is given by m'(t) = 27te^{3t}, where t is time in days. What is the total accumulated growth during the first 2 days?
- A population grows exponentially, and the population P on the day t is given by P(t) = 25 (1.05^t). a. What is the initial population size? b. What is the growth factor? c. What is the daily percent i
- If P(t) is the size of a population at time t, which of the following differential equations describes linear growth
- Suppose f is an exponential function where f(1) = 2. Write an expression using the information in the problem statement and the 1-unit growth factor, b, to determine the output, f(4) Write an expressi
Explore our homework questions and answers library
Browse
by subject