Question

The population of a city is 270​,000 and is increasing at a rate of 2.25​% each year. Approximately when will the population reach 540​,000?

Answer 1

The population will reach approximately 540,000 in 30.57 years.

Step-by-step explanation:

To find approximately when the population will reach 540,000, we can use the formula for exponential growth. The formula is: P = P0 * (1 + r)^t, where P is the final population, P0 is the initial population, r is the growth rate as a decimal, and t is the time in years. Rearranging the formula to solve for t, we have: t = log(P/P0) / log(1 + r).

Plugging in the given values, we can calculate t: t = log(540,000/270,000) / log(1 + 0.0225) ≈ 30.57 years.

Therefore, the population will reach approximately 540,000 in 30.57 years.

Answer 2

The population will reach 540 000 in 30.8 yr.

The formula for population growth is

P_t = P_0 × e^(rt)

540 000 = 270 000 × e^(0.0225t)

e^(0.0225t) = 2

0.0225t = ln2

t = (ln2)/0.0225 = 30.8