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 66 million cars in a certain
Country, increasing by 0.7% annually. How many years will it take for this country to have 87 million cars?
Round to the nearest year.
A) 39 yr
B) 435 yr
C) 5 yr
D) 30 yr

Question

Quizplus · Accepted Answer

To find the number of years it will take for the population of cars to grow from 66 million to 87 million with an annual growth rate of 0.7%, we use the formula $N = Ie^{kt}$. Here, $N = 87$ million, $I = 66$ million, $k = 0.007$ (since 0.7% = 0.007), and $t$ is what we're solving for. Rearranging the formula to solve for $t$, we get $t = \frac{\ln(N/I)}{k}$. Plugging in the values, $t = \frac{\ln(87/66)}{0.007}$, which approximately equals 39 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 $\mathrm { N } = \mathrm { Ie }^ { kt } , \mathrm { N }$