Chapter 5, Problem 13RE

Population Model The population of a certain country is growing exponentially. The total population (in millions) in $t$ years is given by the function $P\left(t\right)$. Match each of the following answers with its corresponding question.

Answers

a. Solve $P\left(t\right)=2$ for $t$

b. $P\left(2\right)$

c. $P^{\prime }\left(2\right)$

d. Solve $P^{\prime }\left(t\right)=2$ for $t$

e. $y\text{'}=ky$

f. Solve $P\left(t\right)=2P\left(0\right)$ for $t$

g. $P_0{}^{e^{kt}}$, k > 0

h. $P\left(0\right)$

Questions

A. How fast will the population be growing in $2$ years?

V. Give the general form of the function $P\left(t\right)$.

C. How long will it take for the current population to double?

D. What will be the size of the population in $2$ years?

E. What is the initial size of the population?

F. When will the size of the population be $2$ million?

G. When will the population be growing at the rate of $2$ million people per year?

H. Give a differential equation satisfied by $P\left(t\right)$.