Question

Please help!!

Write an exponential function (in terms of x) to model the following situation.
A population of 110,000 grows 5% per year for 16 years.
How much will the popluation be after 16 years?

Answer 1

The population will be 240,116

Explanation:

Exponential growth can be represented by the expression:

`P(t) = P_i\,(1+r)^t`

where:

`P(t)` is the population at time (t)

`P_i` is the initial value of the population

"r" is the annual rate of growth (written in decimal form)

and "t" is the time in years.

Therefore in this situation, P(16) is what we want to find [the population after 16 years]

the initial population
`P_i` is 110,000

the rate of growth is 0.05 [decimal form of 5%]

and t is 16 years.

Replacing all these in the given functional form gives:

`P(t) = P_i\,(1+r)^t\\P(16)=110000\,(1+0.05)^16\\P(16)=240116`