Final answer:
The balance of Ella's savings account after 4 years, using the function Bt = 2500 x e^0.025t, is calculated to be approximately $2762.92, with the given options showing a nearest, yet not exact, value of $2662.50 (option c). There may be a typo in the provided options since none of them precisely match the calculated result.
Step-by-step explanation:
To determine the balance of Ella's savings account after 4 years using the given exponential function Bt = 2500 x e^0.025t, we need to substitute the time variable t with the number 4. The formula calculates the future value of an investment or savings over time at a continuous compound interest rate. The variable t represents the number of years, and e is Euler's number, the base of natural logarithms which is approximately equal to 2.71828.
Now, we will calculate:
B4 = 2500 x e^(0.025*4)
This calculation will give us the future balance of the savings account after 4 years, which can be computed using a scientific calculator or a computer software that can handle exponential functions.
Let's perform the calculation:
- B4 = 2500 x e^(0.025*4)
- B4 = 2500 x e^(0.1)
- B4 = 2500 x 1.10517091808 (using the approximate value of e raised to the power of 0.1)
- B4 = 2762.92
Therefore, the future balance after 4 years will be approximately $2762.92, which is closest to option (c) $2662.50, given the choices provided. It seems that there may be a typo in the provided options since none of them matches the calculated result exactly.