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

Question

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?

Clara Addison · Accepted Answer

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

Year 1: 20 (increase) Year 12: 120 (total number) Rate of increase: 0.20, 20%, or 20/100 Years 2–4 = 1.2120 = 144 (total koalas) Years 3–4 = 1.2144 = 173 (total koalas) Years 4–6 = 1.2173 = 208 (total koalas) Years 5–6 = 1.2*250 = 300 In answer to the first part of the question, 300 koalas must be seen in six years. An anaconda comes to the area and eats 80 koalas a year. After the anaconda is present, the following calculations are made: 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 = 100 (living koalas) 6th year = (1.2*100) - 80 = 40 (living koalas) 7th year = (1.2*100) - 80 = 40 (living koalas) Presently, all koalas will be eaten by the anaconda.

Ivy Ackerman · Answer

undefined Sure, I can help with that. To solve a basic population growth problem using calculus, you can use the differential equation for exponential growth or decay, which is:

dP/dt = k * P

Where:
- dP/dt is the rate of change of the population with respect to time
- k is the growth or decay constant
- P is the population size

To solve this equation, you can separate variables and integrate both sides. If you have a specific problem you'd like help with, please provide the details.