Question

A grey squirrel population was introduced in a certain county of Great Britain 35 years ago. Biologists observe that the population doubles every 7 years, and now the population is 60,000.

(a) What was the initial size of the squirrel population?

Answer 1

To find the initial size of the grey squirrel population, we used the exponential growth formula. After calculating, we determined that the initial population size was 1,875 squirrels.

Step-by-step explanation:

The student asked how to find the initial size of a grey squirrel population that doubles every 7 years and now has a population of 60,000 after 35 years.

To calculate the initial population size, we'll use the formula for exponential growth: P(t) = P0 × (2t/T), where P(t) is the population at time t, P0 is the initial population size, 2 is the base because the population doubles, t is the number of years, and T is the time it takes for the population to double.

The problem gives us 35 years (t) and a doubling time (T) of 7 years. Plugging these into the equation, we have 60,000 = P0 × (235/7). Simplifying, we get 60,000 = P0 × 25 or 60,000 = P0 × 32. Dividing both sides by 32, we find the initial population size is 1,875 squirrels.

Thus, the initial size of the grey squirrel population was 1,875.

Answer 2

if this occurred over a span of 35 years and the population doubles every 7 years, we can divide 35 by 7 to find how many times the population has doubled, which would be 5 times. If we divide 60,000 by 2 (or multiply by 1/2) 5 times, you would get the answer, which would be 1,875.