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?

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Answer 1 · 2018-04-25T11:19:18

See 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 $35,836$ . **