Question

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

Answer 1

2024

Explanation:

took the test

Answer 2

Population in 2010, P(o) = 1,405,233
Rate of decrease, R = 1.1% = 0.011

Applicable formula

P(n) = P(o) *(1-R)^n

Where P(n) = population after n years, n = Number of years
From information given,
1,200,000 = 1,405,233 (1-0.011)^6
1,200,000/1,405,233 = (0.989)^n
0.85395 = (0.989)^n
ln (0.85395) = n ln (0.898)
n = [ln (0.85395)]/[ln (0.989)] = 14.27 years ≈ 14 years
Year in which population will fall below 1,200,000 = 2010+14 = 2024

Then, the correct answer is a.