§1.3 The derivative of a function at a point (continued)

Summary

China's population is modeled by $P(t) = 1.15(1.014)^t$ billion people with $t$ years since the start of 1993. What is the average rate of change of the population over $[0, 7]$?

A function satisfies $f(1) = 2.5$, $f(2) = 3.25$, and $f(3) = 3.625$. Using a central difference at $a = 2$, the estimate of $f'(2)$ is

For a position function $s$, which quantity gives the average velocity over the interval $[a, b]$?

With $P(t) = 1.15(1.014)^t$ billion people, compute the total change in population between the start of 1993 and the start of 2000. Give your answer in billions of people, rounded to four decimal places.

The same model $P(t) = 1.15(1.014)^t$ gives an average growth rate of about $0.02234$ billion people per year over the decade from $t = 19$ to $t = 29$. Over how many years was that average computed?

For $P(t) = 1.15(1.014)^t$, the instantaneous growth rate at the start of 1993 is $P'(0) = \displaystyle\lim_{h \to 0} \frac{P(h) - P(0)}{h}$.