Question

At the beginning of a population study, a city had 370,000 people. Each year since, the population has grown by 8.2%. Let t be the number of years since start of study. Let y be city's population. Write an exponential function showing the relationship between y and t

Answer 1

Answer: y = 370000(1.082)^t

Explanation:

We would apply the formula for exponential growth which is expressed as

A = P(1 + r)^t

Where

A represents the population after t years.

t represents the number of years.

P represents the initial population.

r represents rate of growth.

From the information given,

A = y

P = 370000

r = 8.2% = 8.2/100 = 0.082

Therefore, the exponential function showing the relationship between y and t is

y = 370000(1 + 0.082)^t

y = 370000(1.082)^t