# Precalculus

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A ship embarked on a long voyage. At the start of the voyage, there were 500 ants in the cargo hold of the ship. One week into the voyage, there were 800 ants. Suppose the population of ants is an exponential function of time.

(a) How long did it take the population to double?

(b) How long did it take the population to triple?

(c) When were there be 10,000 ants on board?

(d) There also was an exponentially-growing population of anteaters on board. At the start of the voyage there were 17 anteaters, and the population of anteaters doubled every 2.8 weeks. How

long into the voyage were there 200 ants per anteater?

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##### Solution Summary

This solution is comprised of a detailed explanation of how to calculate length of time with regards to exponential population growth. Calculations are done step-by-step for clarity.

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Let the exponential growth model be N(t) = N0 e^kt, where t is in weeks

By data, N0 = 500, so N = 500 e^kt

Also, N(1) = 500 e^k = 800 by data

e^k = 800/500 = ...

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