Question

Can someone help me with this calculus population growth problem? I think I need to use a basic population growth equation.

Koala bears live on a farms land in Australia. The population's rate of growth is determined by the equation dK/dt = yK, where y is constant. The initial population is 100 and after one year, 120 koalas are present. Use this to find out how long it will take the population to increase from 100 to 300 koalas. Once the population reaches 300, a Koala-eating anaconda begins eating koalas, at a rate of 80 koalas every year. How long will it take until all the koalas are gone?

Answer 1

to reach 300, you have to observe koalas for 6 (full) years.

Explanation:

1st year: 20 (increase) Total number at the end of year: 120
Rate of increase is 0.20 or 20% or 20/100
2nd year= 1.2120 = 144 (total koalas)
3rd year=1.2144 = 173 (total koalas)
4th year = 1.2173 = 208 (total koalas)
5th year= 1.2208 = 250
6th year = 1.2*250 = 300

The first part of the question, you need 6 years to see 300 koalas.

An anaconda moves to the area, consuming 80 koalas per year.
After anaconda's presence:
1st year = (1.2300) - 80 = 280 (living koalas)
2nd year = (1.2280) - 80 = 256 (living koalas)
3rd year = (1.2256) - 80 = 227 (living koalas)
4th year = (1.2227) - 80 = 192 (living koalas)
5th year = (1.2192) - 80 = 150 (living koalas)
6th year = (1.2150) - 80 = 100 (living koalas)
7th year = (1.2*100) - 80 = 40 (living koalas)
Before 8th year, all koalas will be consumed by the anaconda. Keep it simple and 7.5 years after first appearance of the anaconda, all koalas will be eaten up by this anaconda.