Question

A ship embarked on a long voyage. At the start of the voyage, there were 400 ants in the cargo hold of the ship. One week into the voyage, there were 700 ants. Suppose the population of ants is an exponential function of time. (Round your answers to two decimal places.) (a) How long did it take the population to double?

Answer 1

1.24 weeks

Explanation:

The ant population a(t) can be modeled by ...

a(t) = 400·(700/400)^t . . . . . where t is in weeks

The population will have doubled when a(t) = 800, so we want to find t for ...

800 = 400·(7/4)^t

2 = (7/4)^t . . . . . . . . . . . divide by 400

log(2) = t·log(7/4) . . . . . take the log

t = log(2)/log(7/4) ≈ 1.2386 ≈ 1.24 . . . . . weeks

It took about 1.24 weeks for the population to double.