Question

2. Answer each of the following based on the scenario below.

Scenario: You bought a car this year for $13,000. Unfortunately your car loses 25% of
-
its value every year.
a.
Does this scenario represent exponential growth or decay? Decay
b. What is the initial value of your savings account?$13,000
aishof wolse Hadapterit
c. What is the growth/decay factor? 25
d. Create a function in exponential form that models how much your car will be worth after x
year.
f(x) =
e. After 3 years how much will your car be worth?
f. After 8 years how much will your car be worth?

Answer 1

correct, is Decay and the initial amount is 13000, rate is 25%

`\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^x\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &13000\\ r=rate\to 25\%\to (25)/(100)\dotfill &0.25\\ x=years \end{cases} \\\\\\ A=13000(1 - 0.25)^(x)\implies \boxed{A=13000(0.75)^x} \\\\\\ \stackrel{\textit{after 3 years}}{A=13000(0.75)^3}\implies A\approx 5484.38~\hfill \stackrel{\textit{after 8 years}}{A=13000(0.75)^8}\implies A\approx 1301.47`