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Question: Yasemin deposited into a savings account. The relationship between the time, , in years, since the account was first opened, and Yasemin's account balance, , in dollars, is modeled by the following function. B(t) = 1000 times e^0.03t How many years will it take for Yasemin's account balance to reach 1500 ? Round your answer, if necessary, to the nearest hundredth.
To solve this problem, we need to solve the formula for time (t) when the balance (B) equals 1500. Here's how to do it: First, let's set B(t) equal to 1500: 1500 = 1000 * e^(0.03 * t) Then divide both sides by 1000: 1.5 = e^(0.03 * t) Taking the natural log (ln) of both sides: ln(1.5) = 0.03 * t Then solve for t: t = ln(1.5) / 0.03 When you calculate this using a calculator, you will get: t ≈ 13.51 So, it will take approximately 13.51 years for Yasemin's account balance to reach 1500 dollars.
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