Question

The number of elk living in a national park can be modelled by the exponential equation y=145(0.985)ˣ

where y represents the number of elk and x represents the time, in years, after 2010. Estimate, using the given function, the elk population in 2030.

Answer 1

To estimate the elk population in 2030, the time span from 2010 to 2030 is calculated as 20 years and substituted into the equation y=145(0.985)^x, resulting in an estimated population of approximately 97 elk.

Step-by-step explanation:

To estimate the elk population in 2030 using the given exponential equation, we need to calculate the number of years after 2010 that 2030 is. The year 2030 is 20 years after 2010, so we will substitute x with 20 in the equation y=145(0.985)^x.

Therefore, the calculation will be as follows:

y = 145(0.985)^20

We compute this using a calculator to get the estimated elk population.

Using a calculator, we find that:

y = 145(0.985)20 ≈ 145 * 0.667853233) ≈ 96.838

This means that the estimated elk population in 2030 would be approximately 97 elk.