Question

In 2005, the population of a state was 31,006,000. If the population grows at 1.2% per year, approximately how
many years (from 2005) will it take the population to reach 40,000,000? (Assuming it grows at the same rate)
use the continuous growth function:
A=pen

150 years
249 years
21 years
26 years

Answer 1

Answer:

Step-by-step explanation:

Answer 2

      Population of the state will reach 40,000,000 in 21 years from year 2005.

      Option (3) will be the correct option.

Exponential growth of the poulation:

•  Exponential growth for the population growth is given by the expression,

          F = I(1 + r)ⁿ

          Here, F = Final population

                    I = Initial population

                    r = Growth rate

                    n = Number of years for population growth

Given in the question,

• Initial population = 31006000

• Growth rate = 1.2%
• Final population = 40000000

To find the number of years for population growth, substitute the values,

F = I(1 + r)ⁿ

40000000 = 31006000(1 + 0.012)ⁿ

40000 = 31006(1.012)ⁿ

$(1.012)^n=\frac{40000}{31006}$

$\text{log}(1.012)^n=\text{log}(1.29)$

nlog(1.012) = log(1.29)

0.00518n = 0.11059

n = $\frac{0.11059}{0.00518}$

n = 21.34

n ≈ 21 years

     Therefore, population of the state will reach 40,000,000 in 21 years from 2005. Option (3) will be the answer.

Learn more about the exponential degrowth here,

https://brainly.com/question/25704728?referrer=searchResults