Question

A city's population is currently 24,000 and is growing by 1.8% each year. If this continues, in how many years will the town's population reach 56,000?

Answer 1

Initial population (P): 24,000

Growing rate per year(r) : 1.8 % = 0.018 in decimal form ( divided by 100)

We have to apply the poupulation growth formula:

A = P (1+ r )^t

Where :

A = population after t years

t= years

Replacing with the values given:

56,000 = 24,000 (1+0.018)^t

Solve for t:

56,000/24,000 = 1.018 ^t

7/3 = 1.018^t

Apply ln to both sides:

ln 7/3 = ln 1.018 ^t

ln 7/3 = t (ln 1.018)

ln 7/3 / ln 1.018 = t

t= 47.49 = 47 years and a half