MATH SOLVE

2 months ago

Q:
# 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

Accepted Solution

A:

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.

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.