Question

The world population1 , in billions, was approximately , where is in years since April 20, 2014. At what rate was the world's population increasing on that date? Give your answer in millions of people per year, rounded to one decimal place.

Answer 1

Answer:

76.3 millions of people per year

Step-by-step explanation:

Missing text of the question:

"The world population1 , in billions, was approximately

$P=7.17e^{0.01064t}$

where t is in years since April 20, 2014. At what rate was the world's population increasing on that date? Give your answer in millions of people per year, rounded to one decimal place."

Answer:

The expression that gives us the world population in billions t years after April 20, 2014 is

$P=7.17e^{0.01064t}$

Where t is expressed in years.

Here we want to find the rate of change of this function at that date.

The rate of change of a function is given by its derivative. Therefore, we have to calculate the derivative of the function P, and the calculate its value at the date indicated.

The derivative of the function is:

$P'(t)=7.17 \cdot 0.01064 e^{0.01064 t}=0.0763 e^{0.01064t}$

Now we want to find the rate of change at the date April 20, 2014, which means zero years after that date; so we have to substitute t = 0 into the expression of the derivative, and we find:

$P'(0)=0.0763e^0 = 0.0763$

So, 0.0763 billions, which corresponds to 76.3 millions of people per year.