Question

1. find the percent increase/decrease of each exponential function.

a. $y = 2(1.54)^x$
b. $y = 4(0.67)^x$

Explanation:

Step1: Recall exponential form

An exponential function is $y = a(b)^x$, where $b=1+r$. $r$ is the growth/decay rate.

Step2: Solve for part a: find $r$

For $y=2(1.54)^x$, $b=1.54$.
$r = 1.54 - 1 = 0.54$
Convert to percent: $0.54 \times 100\% = 54\%$ (increase, since $r>0$)

Step3: Solve for part b: find $r$

For $y=4(0.67)^x$, $b=0.67$.
$r = 0.67 - 1 = -0.33$
Convert to percent: $-0.33 \times 100\% = -33\%$ (decrease, since $r<0$)

Answer:

a. 54% increase
b. 33% decrease