# Algebra

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Solve.

The population of a particular city is increasing at a rate proportional to its size. It follows the function P(t) = 1 + ke^0.12t where k is a constant and t is the time in years. If the current population is 15,000, in how many years is the population expected to be 37,500? (Round to the nearest year.)

• Algebra -

solve
37500 = 1 + 15000(e)^.12t

(the 1 is rather ineffectual in this equation. Are you sure you typed it right way? )

Anyway, assuming it is correct

= 36499 = 15000(e)^.12t
2.4332667 = e^.12t
.12t = ln 2.4332667
.12t = .889235
t = 7.41 yrs or
in appr 7 years

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