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 0.017. 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 0.017. 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

We can use the exponential growth model to calculate the population in 2013:

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 time elapsed since 2000.

We are given that P0 = 11eaa595_6532_a7ba_a696_67ff12d7ad95_TB4584_11_TB4584_11 = 64.07 million, r = 0.017, and t = 13 - 11 = 2 years (since we want to know the population in 2013, which is 13 years after 2000). Plugging these values into the formula, we get:

P(2) = 64.07 e^(0.017*2) = 70.61 million

Rounding to two decimal places, we get:

P(2) ≈ 88.92 million

Therefore, the best choice is D, 88.92 million.

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