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9th grade algebra?
Predict how long it will take for the population to reach 500.
- 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
- BryceLv 72 months ago
t≈ 5.71 years
- Anonymous2 months ago
That would be a 5th grade question when I went to school.