Question

the size of the red squirrel population has decreased exponentially over the past few years in the past few years in the uk. The rate of decrease is 15% per year. At the start of 2016 there were an estimated 10000 red squirrels in the uk. Estimate the size of the population of red squirells at the start of 2010. Give your answer to three significant figures

Answer 1

26,500 squirrels

Explanation:

To estimate the size of the red squirrel population at the start of 2010, we can use the exponential decay formula:

`P(t) = P_0\cdot (1 - r)^t`

where:

• P(t) is the population size at time t.
• P₀ is the initial population size when t = 0.
• r is the annual decrease rate in decimal form.
• t is the number of years elapsed since t = 0.

In this case, P₀ is the population of red squirrels at the start of 2010.

Therefore, t = 0 at the start of 2010, so t = 6 at the start of 2016.

Since we need to find P₀, we can substitute the given values for the population at the start of 2016 into the formula:

• P(t) = 10,000
• r = 15% = 0.15
• t = 6

Therefore:

`10000 = P_0\cdot (1 - 0.15)^6`

`10000 = P_0\cdot (0.85)^6`

`10000 = P_0\cdot 0.377149515625`

`P_0=(10000)/(0.377149515625)`

`P_0=26514.68339665...`

`P_0=26500\; \sf (3\;s.f.)`

So, the estimated size of the red squirrel population at the start of 2010 is approximately 26,500 squirrels (rounded to three significant figures).