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^(0.025 t) What will the balance of Ella's savings account be after 4 years? Round your answer, if necessary, to the nearest hundredth. $

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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^(0.025 t) What will the balance of Ella's savings account be after 4 years? Round your answer, if necessary, to the nearest hundredth.  $

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Identify Given Information: Identify the given information and the formula to use. We are given the initial deposit amount ($2500), the annual interest rate in the form of an exponential growth rate (0.025), and the time period (4 years). We will use the exponential growth formula B(t) = 2500 * e^(0.025 * t) to calculate the balance after 4 years.Substitute Values into Formula: Substitute the given values into the formula. We need to substitute t = 4 into the formula to find B(4), which represents the balance after 4 years. B(4) = 2500 * e^(0.025 * 4)Calculate Exponent Part: Calculate the exponent part of the formula. 0.025 * 4 = 0.1 Now we have B(4) = 2500 * e^0.1Calculate Value of e^0.1: Calculate the value of e^0.1. Using a calculator, we find that e^0.1 ≈ 1.105170918Multiply Initial Amount: Multiply the initial amount by the calculated exponential factor to find the balance. B(4) = 2500 * 1.105170918 B(4) ≈ 2762.927295Round to Nearest Hundredth: Round the result to the nearest hundredth as instructed. B(4) ≈ $2762.93

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