Question

Ella deposited $2500 into a savings account. The relationship between the time, 't', in years since the account was first opened, and Ella's account balance, 'b(t)', in dollars, is modeled by the following function. 'b(t) = 2500 * e^(0.025t)'. What will the balance of Ella's savings account be after 4 years? Round your answer, if necessary, to the nearest hundredth.

Options:
a) $2820.49
b) $2800.00
c) $2923.56
d) $2789.33

Answer 1

The balance of Ella's savings account after 4 years is approximately $2762.93.

Step-by-step explanation:

To find the balance of Ella's savings account after 4 years, we can substitute t = 4 into the function b(t) = 2500 * e^(0.025t). Using a calculator or a computing tool, we can evaluate this expression to find the answer.

Plugging in t = 4 into the function, we get:

b(4) = 2500 * e^(0.025 * 4)

b(4) = 2500 * e^(0.1)

Using a calculator or a computing tool, we can find that the value of e^(0.1) is approximately 1.10517. Multiplying this value by 2500 gives us the balance:

b(4) ≈ 2500 * 1.10517 = 2762.93

Rounding this answer to the nearest hundredth, the balance of Ella's savings account after 4 years is approximately $2762.93.