Question

Write an equation to model the fish population y in a fishery that has a linear growth rate of 40 new fish each season x, and an initial population of 1250 fish.

a) y = 40x + 1250

b) y = 1250x + 40

c) y = 40x - 1250

d) y = 1250 - 40x

Answer 1

The fish population in the fishery is modeled by the linear equation y = 40x + 1250, where x represents each season and y is the fish population, making the correct answer a) y = 40x + 1250.

Step-by-step explanation:

To model the fish population y in a fishery with a linear growth rate of 40 new fish each season x and an initial population of 1250 fish, we use the general equation of a line, y = mx + b, where m is the slope representing the growth rate and b is the y-intercept representing the initial quantity.

Given that each season there is an increase of 40 fish, this would be our slope (m=40). The initial population of 1250 fish represents our y-intercept (b=1250). Thus, the equation to model the fish population would be:

y = 40x + 1250

Therefore, the correct answer is a) y = 40x + 1250.