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Since January 1, 1960, the population of a city has been described by the formula $P=36000(0.95)^t$, where $P$ is the population of the city $t$ years after the start of 1960. At what rate was the population changing on January $1, 1977$?

How do I calculate the rate of the population change?

Key Flex
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Peter Ferri
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  • Are you familiar with the derivative of a function? Could you compute $ \frac{dP}{dt} $? – Ben Oct 24 '18 at 02:23

1 Answers1

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Given $P=36000(0.95)^t$

Now, $\dfrac{dP}{dt}=36000\times\ln(0.95)\times(0.95)^t$

After $t=1977-1960=17$ years,

$$\dfrac{dP}{dt}=\mbox{ rate }=36000\times\ln(0.95)\times(0.95)^{17}\dfrac{\mbox{ people}}{\mbox{ year}}$$

Key Flex
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