Solve the problem.
-In the formula $\mathrm{N}=\mathrm{Ie}^{\mathrm{kt}}, \mathrm{N}$ is the number of items in terms of an initial population $\mathrm{I}$ at a given time $t$ and $k$ is a growth constant equal to the percent of growth per unit time. How long will it take for the population of a certain country to double if its annual growth rate is $6.7 \%$ ? Round to the nearest year.
A) $30 \mathrm{yr}$
B) $4 \mathrm{yr}$
C) $1 \mathrm{yr}$
D) $10 \mathrm{yr}$

Question

Quizplus · Accepted Answer

To find the time it takes for the population to double, use the formula $N = Ie^{kt}$. Set $N = 2I$ and solve for $t$:  $2I = Ie^{0.067t}$  $2 = e^{0.067t}$  Taking the natural logarithm of both sides:  $\ln(2) = 0.067t$  $t = \frac{\ln(2)}{0.067} \approx 10.35$  Rounding to the nearest year gives $10$ years.

Solve the Problem N=Iekt,N\mathrm{N}=\mathrm{Ie}^{\mathrm{kt}}, \mathrm{N}N=Iekt,N Is the Number of Items in Terms of an Initial

Solve the Problem $\mathrm{N}=\mathrm{Ie}^{\mathrm{kt}}, \mathrm{N}$ Is the Number of Items in Terms of an Initial