Question

The population of a small town is growing at a rate of 5% per year. If the population right now is 22,000, what will the population be 10 years from now?

Answer 1

See explanation.

Explanation:

The numbers representing the population in consecutive years create a geometrical sequence with:

`a_1=22,000`

and

`q=1+0.5=1.05`

We are asked to find the popiuation after `10` years. This number is the eleventh term in the sequence, so we are looking for:

`a_11=a_1*q^10=22,000*(1.05)^10`

After substitution of given data we have:

`a_11~~35,836`

Answer:

After 10 years the population will be `35,836`.