The population of a colony of mosquitoes grows exponentially

The population of a colony of mosquitoes grows exponentially according to the function P(t) = P0ekt . How long will it take the colony to reach 10,000 mosquitoes?

Solution

P(t) = P(0)e^(kt)

since P(t)=10,000

Therfore, 10,000=P(0) e^(kt)

=> e^(kt)=10,000/P(0) => kt=ln[10,000/P(0)]

Therfore, t=(1/k)ln[10,000/P(0)]

Since in the given qauestion no initial information is given so we can not find exact value.

if the initial information is given, we can can put P(0) and value of k