Question

Biologists notice an alarming trend in the walleye population in Lake Erie. Despite efforts, the population is decreasing by 15% each year. They estimate the walleye population was 26 million at the beginning of the current year. Write a sequence that lists the population for the first 4 years using 26 million as the first term.

Answer 1

Given:

The initial population is p = 26 million.

The decreasing percentage is r = 15% each year = 0.15.

The objective is to write the sequence of population after 4 years.

Step-by-step explanation:

The general formula of population decrease is,

`A=P(1-r)^t\text{ . . . . .(1)}`

The population in the 1st-year can be calculated by substituting t=1 in equation (1).

`\begin{gathered} A_1=26(1-1.15)^1 \\ =26(0.85) \\ =22.1\text{million} \end{gathered}`

The population in the 2nd year can be calculated by substituting t=2 in equation (1).

`\begin{gathered} A_2=26(1-0.15)^2 \\ =26(0.85)^2 \\ =18.785million \end{gathered}`

The population in the 3rd year can be calculated by substituting t=3 in equation (1).

`\begin{gathered} A_3=26(1-0.15)^3 \\ =26(0.85)^3 \\ =15.967255million \end{gathered}`

Hence, the population for the first 4 years will be,

26million,

22.1million,

18.785million,

15.967255million.