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