Question

jeremiah deposited $350 into a savings account. the savings account balance grows 3.6% each year. write an exponential function to model the balance of jeremiah’s account, y, after x years. y = \square

Explanation:

Step1: Recall exponential growth formula

The standard exponential growth model is $y = a(1 + r)^x$, where $a$ is the initial amount, $r$ is the annual growth rate (in decimal), and $x$ is time in years.

Step2: Identify given values

Initial deposit $a = 350$, annual growth rate $r = 3.6\% = 0.036$.

Step3: Substitute values into formula

Substitute $a=350$ and $r=0.036$ into the model:
$y = 350(1 + 0.036)^x$

Step4: Simplify the growth factor

Calculate $1 + 0.036 = 1.036$, so the function becomes:
$y = 350(1.036)^x$

Answer:

$y = 350(1.036)^x$