Question

Write an exponential function to model the following situation.

A population of 110,000 grows 4% per year for 15 years.
how much will the population be after 15 years?

Answer 1

For 15 years -
`110,000(1.04)^(15)`

After 15 years -
`110,000(1.04)^(x+15)`

Explanation:

We have that,

Initial population is 110,000 which grows by the rate 4% i.e. 0.04 for 15 years.

Since, the exponential growth is given by
`P(1+r)^(x)`,

where P is the initial population, r is the rate of interest and x is the number of years.

Thus, the required population is
`110,000(1+0.04)^(15)` i.e.
`110,000(1.04)^(15)`.

Moreover, after 15 years i.e. x+15 years, the population will be
`110,000(1.04)^(x+15)`.

Thus, the population after 15 years is
`110,000(1.04)^(x+15)`.