In the formula N $\mathrm { N } = \mathrm { Ie }^ { kt }$ , 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 5.7%? Round to the nearest year.
A) 8 yr
B) 19 yr
C) 53 yr
D) 1 yr

Question

Quizplus · Accepted Answer

To find the time it takes for the population to triple, we set N = 3I (since tripling the population means the final population is three times the initial population). The formula becomes $3I = Ie^{0.057t}$. Simplifying, we get $3 = e^{0.057t}$. Taking the natural logarithm of both sides gives $\ln(3) = 0.057t$. Solving for $t$, we find $t = \frac{\ln(3)}{0.057}$, which approximately equals 19 years when rounded to the nearest year.

In the Formula N N=Iekt\mathrm { N } = \mathrm { Ie }^ { kt }N=Iekt

In the Formula N $\mathrm { N } = \mathrm { Ie }^ { kt }$