Question

At the beginning of a population study, a city had 240,000 people. Each year since, the population has grown by 9.7%.

Lett be the number of years since start of the study. Let y be the city's population.
Write an exponential function showing the relationship between y and t.

Answer 1

y(t) = 240,000 x ( 1 + 0.097)∧t

Explanation:

y(1) = 240,000 x ( 1 + 0.097)

y(2) = 240,000 x ( 1 + 0.097) x (1 + 0.097) =240,000 x ( 1 + 0.097)²

y(3) = 240,000 x ( 1 + 0.097) x (1 + 0.097) x ( 1 + 0.097) = 240,000 x ( 1 + 0.097)³

y(t) = 240,000 x ( 1 + 0.097)∧t