Solve the problem.
-In the formula N $$\mathrm { N } = \mathrm { I } \mathrm { e } ^ { \mathrm { kt } }$$ 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 double if its annual growth rate is 6.9%? Round to the nearest year.
A) 29 yr
B) 1 yr
C) 10 yr
D) 4 yr

Question

Quizplus · Accepted Answer

We know that when the population doubles, N = 2I. We also know that k is equal to the percent of growth per unit time, so for an annual growth rate of 6.9%, k = 0.069. Substituting these values into the formula, we get:

2I = I*e^(0.069t)

Simplifying, we get:

2 = e^(0.069t)

Taking the natural logarithm of both sides:

ln(2) = 0.069t

Solving for t, we get:

t = ln(2)/0.069

t ≈ 10.04

Rounding to the nearest year, we get that it will take 10 years for the population to double. Therefore, the answer is choice C.

Solve the Problem N=Iekt\mathrm { N } = \mathrm { I } \mathrm { e } ^ { \mathrm { kt } }N=Iekt

Solve the Problem $\mathrm { N } = \mathrm { I } \mathrm { e } ^ { \mathrm { kt } }$