In the formula N $\mathrm { N } = \mathrm { Ie } ^ { kt } , \mathrm { N }$ 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 72 million cars in a certain
Country, decreasing by 3.4% annually. How many years will it take for this country to have 47 million cars?
Round to the nearest year.
A) 7 yr
B) 95 yr
C) 13 yr
D) 3 yr

Question

Quizplus · Accepted Answer

Given the formula $N = Ie^{kt}$, where $N$ is the final amount, $I$ is the initial amount, $k$ is the rate of growth (or decay, if negative), and $t$ is the time in years. Here, $I = 72$ million, $N = 47$ million, and $k = -0.034$ (since it's a decrease of 3.4% annually, we use a negative sign). We need to solve for $t$. Rearranging the formula and solving for $t$ gives us a value close to 13 years when rounded to the nearest year.

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

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