Question

find the percent increase or decrease that the function models. 9. $y = 148(1.23)^x$ 10. $y = 0.4(0.75)^x$

Explanation:

Step1: Recall exponential growth form

Exponential growth/decay: $y = a(1+r)^x$ where $r$ = rate

Step2: Solve for problem 9's rate

For $y=148(1.23)^x$, $1+r=1.23$
$r = 1.23 - 1 = 0.23$

Step3: Convert to percentage (problem9)

$0.23 \times 100 = 23\%$ (increase, since $r>0$)

Step4: Solve for problem10's rate

For $y=0.4(0.75)^x$, $1+r=0.75$
$r = 0.75 - 1 = -0.25$

Step5: Convert to percentage (problem10)

$|-0.25| \times 100 = 25\%$ (decrease, since $r<0$)

Answer:

1. 23% increase
2. 25% decrease