2. Jin is a wildlife researcher hired to track the population of wolves in the same national park. In Year 1 of the study, there are z wolves; in Year 2 of the study, there are 7 + z wolves; and in Year 3 of the study, there are 3z - 3 wolves. The number of wolves in Year 2 is equal to the number of wolves in Year 3.
a. Write and solve a linear equation to determine the value of z.
I
b. Jin writes an expression to describe the number of wolves in Year 4 of the study. The expression is (x + a)(x - b) where a and b are whole numbers greater than 1 and less than 10. Write an expression that could be the expression Jin uses to describe the number of wolves in the park during Year 4 of the study. Then multiply the two terms of the expression.
a. To find the value of z, we can set the number of wolves in Year 2 equal to the number of wolves in Year 3:
7 + z = 3z - 3
Subtracting z from both sides gives:
7 = 2z - 3
Adding 3 to both sides gives:
10 = 2z
Dividing by 2 gives:
z = 5
Therefore, the initial number of wolves in Year 1 (z) is 5.
b. An expression Jin could use to describe the number of wolves in Year 4 of the study is:
(x + 2)(x - 3)
Now, multiplying the two terms gives:
x^2 - 3x + 2x - 6
= x^2 - x - 6
So, the expression Jin uses for the number of wolves in Year 4 is x^2 - x - 6.