Solve the problem.
-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 2.3%? Round to the nearest year.
A) 1 yr
B) 21 yr
C) 48 yr
D) 130 yr

Question

Quizplus · Accepted Answer

To triple the initial population, we need N = 3I. We can rearrange the formula to solve for t:
N = Ie^(kt)
3I = Ie^(0.023t)   (since the growth rate is given as 2.3%, which is equivalent to 0.023)
3 = e^(0.023t)
ln(3) = 0.023t
t = ln(3)/0.023 ≈ 47.7 years
Rounding to the nearest year gives us 48 years. Therefore, the answer is C.

Solve the Problem N=Iekt\mathrm { N } = \mathrm { Ie } \mathrm { kt }N=Iekt

Solve the Problem $\mathrm { N } = \mathrm { Ie } \mathrm { kt }$