A devastating freeze in January 2007 destroyed roughly 75% of California Central
ID: 3425781 • Letter: A
Question
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.
Explanation / Answer
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