Question

due to an increased use of insecticides the monarch butterfly population in the Midwest is decreasing, the population is one tenth as large as the prior year. The starting population is 100,000write an equation to model the situationwhat will the population be after 5 years

Answer 1

Given that the population is one-tenth as large as the prior year and that the starting population is 100,000, we have the sequence:

a_ 1 = 100000

a_ 2 = 10000

a_ 3 = 1000

a_ 4 = 100

a_ 5 = 10

Then:

In this case, we have r = 1/10 and the equation that models this situation is:

`a_n=100000\left((1)/(10)\right)^(n-1)`

After 5 years, the population will be:

`\:a_5=100000\left((1)/(10)\right)^(5-1)=10\text{ }`