AP Calculus ABhardmcq1 pt
A population grows according to dy/dt = 0.05y. If the initial population is 1000, the population at time t is:
A.1000 + 0.05t
B.1000·(1.05)^t
C.0.05·1000t
D.1000e^0.05t
Explanation
Core Concept
This is exponential growth: dy/y = 0.05dt → ln|y| = 0.05t + C. With y(0) = 1000: C = ln(1000). So y = 1000e^(0.05t).
Correct Answer
D1000e^0.05t
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