Construct Functions from Word Problems

A particular type of cell triples in number every hour. Which function can be used to find the number of cells present at the end of h hours if there are initially 6 of these cells?

• f(h) = 3(6)^h

• f(h) = 6x^h

• f(h) = 6(3)^h

• f(h) = 3(6h)

The amount of cola in a soda machine decreases by a rate of 5% each hour. The amount of cola in the machine was originally 75 gallons. Which function models the amount of cola in gallons after h hours?

• f(h) = 75(-5)^h

• f(h) = -5(75)^h

• f(h) = .95(75)^h

• f(h) = 75(.95)^h

Write an exponential function to model the situation. Then solve. The cost of tuition at a college is $12,000 and is increasing at a rate of 6% per year. Which equations represents this situation?

• C(t) = 1.06(12000)^t

• C(t) = 12000(.06)^t

• C(t) = 12000(.06)^t

• C(t) = 12000(1.06)^t

Write an exponential function to model the situation. You invest $1500. Your investment increases at a rate of 3.5%.

• B(t) = 1500(0.965)^t

• B(t) = 1500(1.035)^t

• B(t) = 1500(.035)^t

• B(t) = 1500(1.965)^t

• David
• Camryn

A pizza shop charges $2.50 for a slice of cheese pizza and an additional $0.50 for each topping. Complete the linear function to show how much money (y) it costs to buy a slice of pizza with x toppings.

y = ​ ​ (a)   x + ​ (b)  

• 0.5

• 2.50

• 1.00

• 1.50

• 2.00

• $33

• $40

• $47

• $53

Write a rule:  A plumber charges $50 for a house call plus $12 per hour for labor.

• y = 50 x + 12

• y = 50 + 12 x

• y = 62 x

• x = 50 + 12y

Sam owes his friend a certain amount of money. The function y = 12x - 40 represents the amount of money that Sam has after he pays his friend back in terms of the number of hours that he works.

How much money does Sam owe his friend?

• $12

• $40

• $y

• $x

Write an exponential function to model the situation. The value of a car is $18000 and is depreciating at a rate of 12% per year.

• V(t) = .88(18000)^t

• V(t) = .12(18000)^t

• V(t) = 18000(.88)^t

• V(t) = 18000(.12)^t