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. There are currently 65 million cars in a certain
Country, increasing by 1.7% annually. How many years will it take for this country to have 81 million cars?
Round to the nearest year.
A) 9 yr
B) 4 yr
C) 13 yr
D) 163 yr

Question

Quizplus · Accepted Answer

First, let's use the given formula to find the growth constant k. We know that the initial population (I) is 65 million and the rate of growth per unit time (k) is 1.7% or 0.017 as a decimal. We can also set N equal to 81 million and solve for t (the time it takes to reach this population).

81 = 65e^(0.017t)
81/65 = e^(0.017t)
ln(81/65) = 0.017t
t = ln(81/65)/0.017 ≈ 12.573

So it will take approximately 12.573 years for the population of cars to reach 81 million. Rounded to the nearest year, the answer is 13 years. Therefore, the best choice is C.

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

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