Exercise 45 Page 287

Let's start by recalling the general formula of exponential growth and exponential decay functions. cc Exponential Growth & Exponential Decay [0.8em] y=a(1+r)^t & y=a(1-r)^tIn both cases a and r are positive numbers. For exponential decay, r is less than 1. Let's rewrite the given function to match one of the above formulas.

g(t)=2(5/4)^t

CalcQuot

Calculate quotient

g(t)=2(1.25)^t

WriteSum

Write as a sum

g(t)=2(1+0.25)^t

Our function matches the format of exponential growth. Here a= 2 and r= 0.25. y= 2(1+ 0.25)^t This means that the rate of growth, also known as the percent of change, is 25 %.