Algebra Function and Domain Word Problem

Question

According to Betty a 2 lb. tenderloin roast put in the oven at 425 degrees will take 45 minutes to cook to medium doneness. A 4 lb. tenderloin at the same temperature will take an hour to reach medium doneness.

a. write a function that models time it takes a tenderloin to roast in terms of the weight of the roast.

b. what is the slope of this function?

c. what is the y-intercept?

d. if a roast weighs 3 lb. how long will it take to cook?

e. if a roast takes 1 hour and 20 minutes to roast, how much does it weigh?

f. what is a reasonable domain for your function?

Answer 1

We will plot this with lb on the x axis, and time on the y axis using these starting equations

Slope = (y2-y1)/(x2-x1)

y = mx + b

a. y = 7.5x + 30 (see b and c)

b. (60min-45min)/(4lb-2lb) = 7.5 min/lb

c. 45 min = (7.5min/lb)(2lb) + b

45 - 7.5*2 = 30 min

d. y = (7.5min/lb)*3lb + 30 min = 52.5min

e. 1hr 20 min = 80 min = (7.5min/lb)x + 30

= 50 min / 7.5 (in/lb) = 6.67 lb

f. Positive x axis (you can only have positive amounts of meat)

hope these help!