# Rewrite the function f(t) = 4(1.25)^(t+3) to determine whether it represents exponential growth...

## Question:

Rewrite the function {eq}f(t) = 4(1.25)^{(t+3)} {/eq} to determine whether it represents exponential growth or exponential decay. Identify the percent rate of change.

## Exponential Growth or Decay Rate

Exponential growth or decay models the growth or the decay of a certain population at a certain rate. To check whether the function is exponentially growing or decaying we will rewrite the function and check it with the standard format which says {eq}y=a(1+r)^t {/eq}, where {eq}r {/eq} is the growth rate or percentage rate of change. For exponential growth, {eq}(1 + r) > 1 {/eq} and for exponential decay, {eq}(1 + r) < 1 {/eq}.

## Answer and Explanation:

Become a Study.com member to unlock this answer! Create your account

View this answerWe are given the function {eq}f(t) = 4(1.25)^{(t + 3)} {/eq} and we are asked to rewrite this function to determine whether it represents exponential...

See full answer below.

#### Ask a question

Our experts can answer your tough homework and study questions.

Ask a question Ask a question#### Search Answers

#### Learn more about this topic:

from

Chapter 19 / Lesson 4Understand what the population growth rate is and different population growth rate formulas in various cases. Learn how to calculate the population growth rate.

#### Related to this Question

- Rewrite the function f(t) = 4(1.25)^t + 3 to determine whether it represents exponential growth or exponential decay. Then identify the percent rate of change.
- 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}
- |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).
- 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.
- Refer to the table to answer the following questions. 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).
- 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 = 2.6e^{0.09t} a) What is the initial quantity? b) What is the growth rate? State if the growth rate is continuous.
- If a function is represented by A = 3500(0.93)^t i) is this an example of exponential growth or decay? ii) what is the percent change each time period?
- 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.
- 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.
- What is the exponential growth or decay of this function and the constant percentage 20(.876)^x
- How do you determine whether the following function represents exponential growth or decay: y=3(5/2)^x
- Assume an exponential function has a starting value of 13 and a growth rate of 0.35%. Write an equation to model the situation.
- Given the following exponential decay functions, identify the decay rate in percentage form. a) y = 300 \cdot 0.654^t . b) A = 8 \cdot 0.995^t . c) N = 75 \cdot 0.72^t .
- Determine if the equation { y = 2^x } represents exponential growth or decay?
- Explain how to identify an exponential growth/decay function on a graph.
- For x greater than or equal to 0, identify each of the following functions as a growth (G) exponential or a decay (D) exponential function. A) y = (1/3)^(0.3x) B) y = (1/4)^(-4x)
- For x greater than or equal to 0, identify each of the following functions as a growth (G) exponential or a decay (D) exponential function. A) y = 4e^(-0.2x) B) y = (1/2)^x
- The table below represents an exponential function. Construct that function and then identify the corresponding growth or decay rate in percentage form. \begin{array}{ll} x & y \\ \hline 0 & 200 \\ 1 & 220\\ 2 & 242 \\ 3 & 266.2\\ \hline \end{array}
- The function: f(x) = 7(2)^x represent exponential growth or decay? What is a? What is b?
- Draw the exponential function, f(x) = e^x, and interpret if it has growth or decay.
- How do you determine if the equation y = 0.25(1.03)^5 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 = 0.5(1.2)^x represents exponential growth or decay?
- Find: The amount of radioactive substance decreases? exponentially, with a decay constant of 4% per month. Write a differential equation to express the rate of change \frac{dy}{dt} =?
- For the graph of g(x)= 4(1.062)^x: What are the growth/decay factor and growth/decay rate?
- Find the relative rate of change f (t) at the given value of t. Assume t is in years and give your answer as a percent. f (t) = 4 t^3 + 12; t = 6 Round your answer to one decimal place.
- The amount of a radioactive substance decreases exponentially with a decay constant of 5% per month. a) Write a differential equation to express the rate of change. Define the variables that you use.
- Give the starting value a, the growth/decay rate r, and the continuous growth/decay rate k. If there Is exponential decay your growth rates should negative. Q = 11.5 . 10^{-0.36 t}.
- Explain the mathematical model for the exponential growth or decay.
- 1) The decay rate of a certain chemical is 9.5% per year. What is its half-life? Use the exponential decay model P(t) = Poe^{-kt} where k is the decay rate, and Po is the original amount of chemical. (Round to the nearest integer.) 2) Solve for x. log_
- How do you determine the multiplier for exponential growth and decay?
- How does the average rate of change differ for a linear function versus an increasing exponential function?
- Each function below describes how something changes. Use the description to determine which function(s) describe exponential growth or decay. Select all that apply. The pollution increases at a rate
- Find the associated exponential decay or growth model. Q = 3,000 when t = 0; doubling time = 2
- Given the exponential function f(x) = A_0 e^{kx} where A_0 is real positive constant and k\in \mathbb{R} . For what values of k does this function represent exponential growth and for what values represents exponential decay?
- Identify the initial amount a and the growth factor b in the exponential function { g(x)=4x^2. }
- 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
- Identify the initial amount and the growth factor b in the exponential function. y= 5(0.5)^x
- (a) What is the continuous percent growth rate for P = 110e^0.07t, with time, t, in years? (b) Write this function in the form P = P0a^t. What is the annual percent growth rate?
- Write an equation for an exponential growth function y=f(x) where the initial population is 6000 and the growth factor is 1.132.
- Write an equation for an exponential growth function y = f(x) where the initial population is 3000 and the growth factor is 1.085.
- The function f(t) = 2600 (1.002)^t represents the change in a quantity over t months. What does the constant 1.002 reveal about the rate of change of the quantity?
- Find the rate of growth of the function { a(x)=19(2.046^x) }
- 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
- The equation y = 400(1.03)^{x} is an example of what? A. Exponential growth B. Exponential decay C. Not exponential
- Explain how to calculate exponential decay from time constant.
- Find the associated exponential decay or growth model. Q = 1,200 when t = 0; half-life = 1
- Find the relative rate of change f' t/f(t) at the given value of t. Assume t is in years and give your answer as a percent. f(t) = 2t^3+8 t = 5
- 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
- The amount of radioactive substance decreases exponentially, with a decay constant of 3% per month. a) Write a differential equation to express the rate of change. b) Find a general solution to the di
- 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.
- The function: f(x) = 4(1/3)^x represent exponential; growth or decay? What is a? What is b?
- The function f(t) = 600(1.009)^{30t} represents the change in a quantity over t months. What does the constant 1.009 reveal about the rate of change of the quantity?
- The exponential function y = 1/3 (3/e)^(-x) is a: a. Decay function b. Growth function. c. None of the choices
- 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
- An exponential growth model has the form ______ and an exponential decay model has the form ______.
- 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
- Years, percent or percent per year Use the exponential decay model, A = A_0 e^{kt}, to solve the following. The half-life of a certain substance is 25 years. How long will it take for a sample of this substance to decay to 84% of its original amount? (Rou
- Find the associated exponential decay or growth model. Q = 2,300 when t = 0; half-life = 2 Q =
- Find the associated exponential decay or growth model. Q = 2,300 when t = 0; half-life = 6 Q =
- Is the function y = 1.46(0.3)^x is an example of exponential growth or decay? Why?
- Let G be an exponential function that is changing at a rate proportional to itself, with a constant of proportionality 0.6. What's the growth factor of G?
- The function: f(x) = 2(3)^x represent exponential growth or decay? What is a? What is b?
- 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.
- Devise the exponential growth function that fits the given data, then answer the accompanying question. Be sure to identify the reference point(t = 0) and units of time. Uranium-238(U-238) has a half
- A chemical substance has a decay rate of 7.5% per day. The rate of change of an amount N of the chemical is given by the equation dN/dt = -0.075 N, where t is the number of days since the decay began.
- A chemical substance has a decay rate of 8.7% per day. The rate of change of an amount N of the chemical is given by the equation dN dt =-0.087 N where t is the number of days since the decay began
- The function f(t) = (780)*0.05^(t/60) represents the change in a quantiy over t minutes. What does the value 0.05 reveal about the rate of change of the quantity?
- Find the relative growth rate of the function f(t)=12(\frac{1}{32})^{0.6t}.
- Write a differential equation that expresses the law of natural growth. What does it say in terms of relative growth rate?
- Devise an exponential decay function that fits the given data, then answer the accompanying question. Be sure to identify the reference point (t = 0) and units of time.
- A chemical substance has a decay rate of 9.3% per day. The rate of change of an amount N of the chemical is given by the equation \frac{dN}{dt} = -0.093N , where t is the number of days since
- Prove that if y = y0ekt, where y0 and k are constants, then dy/dt = ky. (This says that for exponential growth and decay, the rate of change of the population is proportional to the size of the population, and the constant of proportionality is the growth
- The quantity of an exponentially decaying substance decreases by 48% in 10 hours. a. Calculate both the incremental hourly percentage rate of decay and the continuous hourly rate of decay. Give both as a percentage, correct to two decimal places. b. Det
- Does the model y = 120e^-0.25x represent exponential growth or exponential decay?
- Which of the following statements is the best description of exponential decay? A. Exponential behavior occurs when a function increases at a rate of increasing value. B. Exponential behavior occurs when a function increases at a rate of decreasing valu
- The exponential function N = 2500 \times 1.74^d, where d is measured in decades, gives the number of individuals in a certain population. a) Calculate N(1.5). b) What is the percentage growth rate per decade? c) What is the yearly growth factor rounded to
- The quantity of an exponentially decaying substance decreases by 48% in 10 hours. \\ a) Calculate both the incremental hourly percentage rate of decay and the continuous hourly rate of decay. Give bot
- The decay rate of a certain chemical is 9.39.3% per year. What is its half-life? Use the exponential decay model P(t ) = P_0E^{-kt}, where k is the decay rate, and P_0 is the original amount of chemical. The half-life of the chemical is [{Blank}] years.
- Given that a quantity Q(t) is described by the exponential growth function Q(t) = 590e^{0.02t} Q(t) = 590e^{0.02t}
- Let P'(t)=P(t)1- \frac{P(t)}{M} be an equation modeling the rate of change of a population P as a function of time t (in years). Note that the value of this derivative depends on the value of the population at that time, P(t). a) If P(t_o) is much large
- Find: 1) Instantaneous Rate of Change Suppose that the amount in grams of a radioactive substance present at time t (in years) is given by A(t)=660^{e^{-0.58t . Find the rate of change of the quant
- 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
- A chemical substance has a decay rate of 8.8% per day. The rate of change of an amount N of the chemical is given by the equation frac{dN}{dt} = -0.088 N where t is the number of days since decay began. a) Let N_0, represent the amount of the chemical
- Determine the growth and decay factors and the growth and decay rates in the following tables:
- An exponential function f has a 3-unit growth factor of 1.61. What is the 1-unit growth factor for f?
- Use the exponential decay model, A = A_0 e^{kt}, to solve the following. The half-life of a certain substance is 22 years. How long will it take for a sample of this substance to decay to 63 \% of its original amount? It will take approximately \boxed{\
- Does f(t) = 61(25)t represent growth or decay?
- Given the exponential function A(x) = P(1 + r)^x, what value for r will make the function a decay function?
- Assume that f[x] is a power function and that g[x] equals 3 times e to the power of rx where r is a positive number. Then which function f[x] or g[x] posts the larger average percent growth rate for l
- 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
- Given the exponential function: a(x) = p(1 + r)^x, what value for r will make the function a growth function?
- 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
- Make an exponential model y(t) with the given properties. Assume that t is the number of periods. The initial value is 560, and there is a 49% decrease each period.