A devastating freeze in January 2007 destroyed roughly 75 of

A devastating freeze in January 2007 destroyed roughly 75% of California Central Valley\'s orange crop. Market analysts predicted that as a result of the freeze, an orange that cost $0.50 before the freeze would cost $1.50 after the freeze. Model the price c of an orange as a linear function of the percentage p of the crop that was destroyed. (Hint: When 0% of the crop was destroyed, the price was $0.50.)

Determine the vertical and horizontal intercepts of the graph of the implied linear function algebraically.

Solution

ordered pair points as (percent damaged, price). We have two points that are are (0,0.5) and (75,1.5), which you may assign coordinate variables as (p,c).

slope = ( 1.5 - 0.5)/( 75 -0) = 1/75

c = m*p + 0.5

c(p) = p/75 +1/2 ( Model of the price in terms of percentage crop destroyed)

Intercepts: Horizontal intercept plug p =0 ; c = 1/2

Vertical intercepts : plug c =0 ; p = -37.5