In 2010, a city's population was 1,405,233 and it was decreasing at a rate of 1.1%. At this rate when will the city's population fall below 1,200,000?

a. 2024

b. 2027

c. 2036

d. 2049

Question

Mathematics

Terrell Giles

11 February, 06:45

In 2010, a city's population was 1,405,233 and it was decreasing at a rate of 1.1%. At this rate when will the city's population fall below 1,200,000?

a. 2024

b. 2027

c. 2036

d. 2049

+3

Answers (1)

Know the Answer?

Michaela · Answer 1

The equation

P (t) = 1405233 * (1 - 0.011) ^ (t)

models the population at t years after 2010. Then, when P (t) = 1,200,000, we have

1200000 = 1405233 * (0.989) ^t

(0.989) ^t = 1200000/1405233

t = log (1200000/1405233) / log (0.989)

t = 14.27 years

This means 14.27 years after 2010. Therefore, the answer to this question is 2024.

In 2010, a city's population was 1,405,233 and it was decreasing at a rate of 1.1%. At this rate when will the city's population fall below 1,200,000?a. 2024b. 2027c. 2036d. 2049

In 2010, a city's population was 1,405,233 and it was decreasing at a rate of 1.1%. At this rate when will the city's population fall below 1,200,000?

a. 2024

b. 2027

c. 2036

d. 2049