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AP Calculus BC/Unit 7: Differential Equations
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Exponential Growth Model

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Let A(t)A(t) be the amount of money, in thousands of dollars, in an investment account at time tt years. The function AA is differentiable and satisfies the differential equation dAdt=kA \frac{dA}{dt} = kA , where kk is a constant. At time t=0t=0, the account balance is 320 thousand dollars and is increasing at a rate of 80 thousand dollars per year. Which of the following is an expression for A(t)A(t)?

A

320et/4 320e^{t/4}

B

320e80t 320e^{80t}

C

80t+320 80t + 320

D

et/4+319 e^{t/4} + 319

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