Question

The table compares x, the number of minutes of television Sam watched each day, to y, the number of minutes she spent exercising. The function y = –0.78x + 95 models the data in the table.

Which is the best prediction for the number of minutes of exercising Sam will do if she spends 30 minutes watching television that day?

45 minutes
72 minutes
83 minutes
118 minutes

Answer 1

Given:
x = number of minutes of television watched per day
y = number of minutes she spent exercising

f(x) = -0.78x + 95

x = 30 minutes
y = -0.78(30) + 95 = -23.40 + 95 = 71.60 minutes ⇒ 72 minutes

x = 45 minutes
y = -0.78(45) + 95 = -35.10 + 95 = 59.90 minutes ⇒ 60 minutes

x = 72 minutes
y = -0.78(72) + 95 = -56.16 + 95 = 38.84 minutes ⇒ 39 minutes

x = 83 minutes
y = -0.78(83) + 95 = -64.74 + 95 = 30.26 minutes ⇒ 30 minutes

x = 118 minutes
y = -0.78(118) + 95 = -92.05 + 95 = 2.96 minutes ⇒ 3 minutes

Answer 2

For this case we have the following variables:

x: the number of minutes of television Sam watched each day

y: the number of minutes she spent exercising

Then, we have the following function that models the problem:

`image`

if she spends 30 minutes watching television we have x = 30.

Substituting in the given equation we have:

`image`

Answer:

the best prediction for the number of minutes of exercising Sam will do if she spends 30 minutes watching television that day is:

72 minutes