Question

ella deposited $2500 into a savings account.
the relationship between the time, $t$, in years, since the account was first opened, and ellas account balance, $b(t)$, in dollars, is modeled by the following function.
$b(t) = 2500 \cdot e^{0.025t}$
what will the balance of ellas savings account be after 4 years?
round your answer, if necessary, to the nearest hundredth.
$

Explanation:

Step1: Substitute t=4 into function

$B(4) = 2500 \cdot e^{0.025 \times 4}$

Step2: Simplify exponent term

$0.025 \times 4 = 0.1$, so $B(4) = 2500 \cdot e^{0.1}$

Step3: Calculate $e^{0.1}$ and multiply

$e^{0.1} \approx 1.10517$, so $B(4) \approx 2500 \times 1.10517$

Step4: Compute final balance

$2500 \times 1.10517 = 2762.925$

Answer:

2762.93