Suppose that the population (in millions) of a Egypt in 2007 is 80.3 and that expected continuous annual rate of change of the population is The exponential growth model for the population by letting corresponds to 2000 is Use the model to predict the
Population of the country in 2013.Round your answer to two decimal places.
A)83.08 million
B)87.42 million
C)90.45 million
D)88.92 million
E)81.68 million

Question

Suppose that the population (in millions) of a Egypt in 2007 is 80.3 and that expected  continuous annual rate of change of the population is  The exponential growth model for the population by letting  corresponds to 2000 is  Use the model to predict the
Population of the country in 2013.Round your answer to two decimal places.
A)83.08 million 
B)87.42 million 
C)90.45 million 
D)88.92 million 
E)81.68 million

Quizplus · Accepted Answer

Let P(t) be the population (in millions) of Egypt t years after 2000.
According to the problem,
P(7) = 80.3 (population in 2007)
The continuous annual rate of change of the population is r = 6.2% = 0.062 (since the expected continuous annual rate of change is 6.2%)
Using the exponential growth model, we have:
P(t) = P(0)e^(rt)
where P(0) is the population in 2000.
Plugging in the values we know:
80.3 = P(0)e^(0.062*7)
Solving for P(0):
P(0) = 66.84
Therefore, the model for the population is:
P(t) = 66.84e^(0.062t)
To find the population in 2013 (13 years after 2000), we plug in t = 13:
P(13) = 66.84e^(0.062*13) = 88.92 (rounded to two decimal places)
So the predicted population of Egypt in 2013 is 88.92 million. Therefore, the answer is D. We can use the exponential growth model:

P(t) = P0 * e^(rt)

where P0 is the initial population (in 2000), r is the continuous annual rate of change, and t is the number of years since 2000.

We are given P0 = 68.3 and r = 0.019, since the expected continuous annual rate of change is 1.9%.

To predict the population in 2013 (13 years after 2000), we can plug in t=13:

P(13) = 80.3 * e^(0.019*13) = 88.92 million

Therefore, the best choice is D, with a predicted population of 88.92 million.

Suppose That the Population (In Millions) of a Egypt in 2007