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Question

# U.S. Population The Museum of Science in Boston displays a running total of the U.S. population. On May $11, 1993.$ the toxal was increasing at the rate of $1$ person every $14$ sec. The displayed population figure at $3:45$ P.M. that day was $257,313,431$. Assume that the relative growth rate is constant. What is the relative growth rate per year ( $365$ days)?

Solution

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The problem asked to find the relative growth rate per year $(365 \text{ days})$ $k$ using the differential equation for population

$\dfrac{dP}{dt}= kP$

where $\dfrac{dP}{dt}$ is the total increase at the rate of $1$ person every $14$ seconds and the total displayed population that day was $P = 257,313,431$.

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