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# 9th grade algebra?

Predict how long it will take for the population to reach 500.

thank you!

### 3 Answers

- Wayne DeguManLv 71 month ago
Not quite sure whether 'logarithms' are familiar to you in the 9th grade.

We can say, P(t) = 225 x (1.15)ᵗ

The 1.15 part is the annual increase of 15% and t is the time in years.

so, after year 1 we would have 225 x 1.15

after year 2 we would have 225 x 1.15 x 1.15...e.t.c.

After 5 years we have, 225 x 1.15⁵ = 453...to 3 s.f.

After 6 years we have, 225 x 1.15⁶ = 520...to 3 s.f.

so, the population reaches 500 between 5 and 6 years.

If you are ok with logarithms we can say:

500 = 225 x (1.15)ᵗ

so, 1.15ᵗ = 500/225

or, ln(1.15ᵗ) = ln(20/9)

i.e. tln(1.15) = ln(20/9)

Hence, t = ln(20/9)/ln(1.15) => 5.7 years

:)>

- Anonymous2 months ago
That would be a 5th grade question when I went to school.