Question

The amount of money in a savings account after t years is represented by the function f(t)=500(1.015)t.

Answer 1

Answer:

The initial amount in the account is $500.

Step-by-step explanation:

The amount of money in a savings account after t years is represented by the function f(t)=500(1.015)t.

General form of exponential growth function is

$y=a(1+r)^t$

y is the accumulated amount

a is the initial amount in the account

r is the rate of interest

t is the time period

$y=500(1+0.15)^t$

Here 500 is the initial amount in the account.

Answer 2

$\bf \qquad \textit{Amount for Exponential Growth}\\\\ A=I(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ I=\textit{initial amount}\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{elapsed time}\\ \end{cases} \\\\\\ f(t)=\stackrel{\stackrel{I}{\downarrow }}{500}(1.015)^t$