Suppose that the population (in millions) of Paraguay in 2007 was 6.7 and that the expected continuous annual rate of change of the population is 0.024.Find the exponential growth
Model for the population by letting correspond to 2000.Round your answer to four
Decimal places.

Question

Suppose that the population (in millions) of Paraguay in 2007 was 6.7 and that the expected continuous annual rate of change of the population is 0.024.Find the exponential growth
Model  for the population by letting  correspond to 2000.Round your answer to four
Decimal places.

Quizplus · Accepted Answer

Using the formula $P(t) = P_0 e^{rt}$, where $P_0$ is the initial population, $r$ is the continuous annual rate of change, and $t$ is the time elapsed in years, we can find the exponential growth model for the population of Paraguay in 2007 as follows:

$P(t) = 6.7 e^{0.024(t-7)}$

where we subtract 7 from $t$ to correspond to the year 2000.

We can plug in $t=7$ to get the population in 2007:

$P(7) = 6.7 e^{0.024(7-7)} = 6.7$

Therefore, the population in 2007 is correctly given as 6.7 million in the problem statement, so we can use this model to predict the population in future years.

We can use a calculator to find $P(11)$, which corresponds to the year 2011:

$P(11) \approx 6.7 e^{0.024(11-7)} \approx 7.59$

Rounded to four decimal places, this gives us a population of 7.5902 million.

Therefore, the best choice is B.

Suppose That the Population (In Millions) of Paraguay in 2007