Choose the one alternative that best completes the statement or answers the question.
-In the formula N $\mathrm { N } = \mathrm { Ie } ^ { \mathrm { kt } }$ N is the number of items in terms of an initial population 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 triple if its annual growth rate is 7.5%? Round to the nearest
Year.
A) 1 yr
B) 6 yr
C) 40 yr
D) 15 yr

Question

Quizplus · Accepted Answer

To find the time it takes for the population to triple, we use the formula $N = Ie^{kt}$, where $N$ is the final population, $I$ is the initial population, $k$ is the growth rate per unit time (in this case, per year), and $t$ is the time in years. Since we want the population to triple, $N/I = 3$. The growth rate $k = 7.5\% = 0.075$. Substituting these values into the formula gives $3 = e^{0.075t}$. Taking the natural logarithm of both sides to solve for $t$ gives $ln(3) = 0.075t$, leading to $t = ln(3)/0.075$, which approximately equals 14.97 years, rounded to the nearest year is 15 years.

Choose the One Alternative That Best Completes the Statement or Answers