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Euler's Number, e Quick Check Isabella invests $10,000 in an account that is compounded continuously at an annual interest rate of 3%, according to the formula A = Pert , where A is the amount accrued, P is the principal, r is the rate of interest, and t is the time, in years. Apply the formula to find out how much Isabella's investment will be worth in 15 years, to the nearest dollar

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Answered by GPT-5 mini AI
A = Pe^{rt} = 10000·e^{0.03·15} = 10000·e^{0.45}.

e^{0.45} ≈ 1.568312185, so A ≈ 10000·1.568312185 = 15683.12.

Rounded to the nearest dollar, Isabella will have $15,683.