Question

The world’s population is expected to grow at a rate of 1.3% per year until at least the year 2020. In 1994 the total population of the world was about 5,642,000,000 people. Use the formula to predict the world’s population , n years after 1994, with equal to the population in 1994 and i equal to the expected growth rate. What is the world’s predicted population in the year 2020, rounded to the nearest million? Question 2 options:12,632,000,0007,911,000,0007,549,000,0007,317,000,000

Answer 1

Answer: b.7,911,000,000

Explanation:

Answer 2

The answer is 7,911,000,000

EXPLANATION

Problem Statement

The question tells us that the world's population is modeled by the formula:

`\begin{gathered} P_N=P_0e^(iN) \\ \text{where, } \\ i=\text{growth rate of the population} \\ N=\text{Number of years} \\ P_0=\text{Initial population at 1994} \\ P_N=\text{Population at year of interest} \end{gathered}`

Solution

To solve this question, we simply need to plug in all the values given to us. That is,

`\begin{gathered} \text{Growth rate = 1.3 \%} \\ \text{ Initial population (}P_0)=5,642,000,000 \\ \text{Number of years (N) = 2020 - 1994 = 26} \end{gathered}`

Thus, we can find the estimated world population in year 2020 as follows:

`\begin{gathered} P_N=P_0e^(iN) \\ P_N=5,642*10^6* e^{(1.3)/(100)*26} \\ P_n=7,910.88*10^6\approx7,911,000,000\text{ (To the nearest million)} \end{gathered}`

Final Answer

The answer is 7,911,000,000