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}.
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