The cost of implementing an invasive species management system in a forest is re

Question

The cost of implementing an invasive species management system in a forest is related to the area of the forest. It costs $620 to implement the system in a forest area of 10 acres. It costs $1044 in a forest area of 18 acres.

(a) Write a linear equation giving the cost of the invasive species management system in terms of the number of acres x of forest. (Let y be the dependent variable.)

(b) Use the equation in part (a) to find the cost of implementing the system in a forest area of 40 acres.
$__________

Explanation / Answer

(a).Let the linear equation giving the cost of the invasive species management system in terms of the number of acres x of forest be y = mx +c. Then m = (1044-620)/(18-10) = 424/8 = 53 so that y = 53x +c. Now, on substituting x = 10 and y = 620 in this equation, we get 620 = 530+c or, c = 620-530 = 90. Thus, the required linear equation is y = 53x+90.

(b).If x = 40, then y = 53*40 +90 = 2120+90 = 2210. Thus, the cost of implementing the system in a forest area of 40 acres is $ 2210.

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