Solve the problem.
-A certain country's population $\mathrm{P}(\mathrm{t})$, in millions, tyears after 1990 can be approximated by $P(t)=3.495(1.016)^{t}$.
In what year did the country's population reach 4 million?
A) About 1999
B) About 2004
C) About 2009
D) About 1989

Question

Quizplus · Accepted Answer

To find the year when the population reached 4 million, set $P(t) = 4$ and solve for $t$:$$4 = 3.495(1.016)^{t}$$Divide both sides by 3.495:$$\frac{4}{3.495} = (1.016)^{t}$$Take the natural logarithm of both sides to solve for $t$:$$t = \frac{\ln\left(\frac{4}{3.495}\right)}{\ln(1.016)}$$Solving this gives a value of $t$ approximately equal to 9 years after 1990, which is 1999.

Solve the Problem P(t)\mathrm{P}(\mathrm{t})P(t) , in Millions, Tyears After 1990 Can Be Approximated By Millions

Solve the Problem $\mathrm{P}(\mathrm{t})$ , in Millions, Tyears After 1990 Can Be Approximated By Millions