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

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The height of a plant, H(t)H(t), is measured in centimeters at time tt in weeks. The function HH is differentiable and satisfies the differential equation dHdt=kH \frac{dH}{dt} = kH , where kk is a constant. At t=0t=0, the plant’s height is 50 cm and it is growing at a rate of 15 cm per week. Which of the following is an expression for H(t)H(t)?

A

50e15t 50e^{15t}

B

15t+50 15t + 50

C

e3t/10+49 e^{3t/10} + 49

D

50e3t/10 50e^{3t/10}

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