Question

In the following application problems, assume a linear relationship holds. 7) A person who weighs 150 pounds has 60 pounds of muscles; a person that weighs 180 pounds has 72 pounds of muscles. If x represents body weight and y is muscle weight, write an equation describing their relationship. Use this relationship to determine the muscle weight of a person that weighs 170 pounds.
9) A male college student who is 64 inches tall weighs 110 pounds. Another student who is 74 inches tall weighs 180 pounds. Assuming the relationship between male students' heights (x), and weights (y) is linear, write a function to express weights in terms of heights, and use this function to predict the weight of a student who is 68 inches tall.

13) California’s population was 29.8 million in the year 1990, and 37.3 million in 2010. Assume that the population trend was and continues to be linear, write the population function. Use this function to predict the population in 2025. Hint: Use 1990 as the base year (year 0); then 2010 and 2025 are years 20, and 35, respectively.)

15. A college’s enrollment was 13,200 students in the year 2000, and 15,000 students in 2015. Enrollment has followed a linear pattern. Write the function that models enrollment as a function of time. Use the function to find the college’s enrollment in the year 2010. Hint: Use year 2000 as the base year.

17. The cost of electricity in residential homes is a linear function of the amount of energy used. In Grove City, a home using 250 kilowatt hours (kwh) of electricity per month pays $55. A home using 600 kwh per month pays $118. Write the cost of electricity as a function of the amount used. Use the function to find the cost for a home using 400 kwh of electricity per month.

21) Mugs Café sells 1000 cups of coffee per week if it does not advertise. For every $50 spent in advertising per week, it sells an additional 150 cups of coffee.

a) Find a linear function that gives y = number of cups of coffee sold per week x = amount spent on advertising per week.

b) How many cups of coffee does Mugs Café expect to sell if $100 per week is spent on advertising?

Answer 1

Answer:

weight/muscle

y = 0.4x

a 170 pounds will have 68 pounds of muscle

heights/weights

y = 7x-338

68 inches weights 138 pounds

year/college

y = 120  x t + 13,200

beging the base the year 2000 2015 will be t = 15

at t =10   14,400

kwh/ cost

y = 0.18 x + 10

y = 0.18 x 400kwh  + 10 = 82

coffe cups/cost

y = 3 x + 1000

at x = 100

it will sale 1300 coups of coffee

Explanation:

$\\y = ax + b\\\frac{y_2-y_1}{x_2 - x_1} = a$

(72-60)/(180-150) = 12/30 = 0.4

y = ax + b

60 = 0.4 x 150 + b

b = 60-60  = 0

170 x 0.4 + 0 = 68

(180 - 110)/(74 - 64) = 70 / 10 = 7

180 = 7 x 74 + b

b = -338

7x68 - 338 = 138 pounds

(15000 - 13200) /( 2015 - 2000) = 120

13200 + 120 x 10  = 14,400

(118 - 55)/(600 - 250) = 0.18

118 - 0.18 x 600 = b

b = 10

150/0 = 3

y = 3 x + 1000

y = 3 (100) + 1,000 = 1,300