Linear Function in Context

To prepare for a recent road trip, Jill filled up her 19-gallon tank. She estimates that her SUV will use about three gallons per hour. Write an equation to model the amount of gasoline, G, remaining in her tank after t hours.

• G=19 – 3t

• G=19 + 3t

• G=3 - 19t

• G=3 + 19t

At the beginning of October, Monique changed banks and decided to leave the remaining $3900 in her old checking account to pay for rent. After six months, her balance was finally zero. If the balance, B, in Monique’s account is a function of time, t, write an equation for the situation.

• B = 3900 – 650t

• B = 3900 + 650t

• B = 3900t – 650t

• B = 3900t + 650t

On a recent scuba diving trip, Kate and Kara reached a depth of 130 feet. Six-and- a-half minutes later after ascending at a constant rate, they reached the surface. Write an equation to represent their distance, D, as a function of time, t.

• D = 130 – 20t

• D = 130 + 20t

• D = 20 – 130t

• D = 20 + 130t

Cedric and Josh both ordered the same size pizzas at Marco’s Pizzeria; however, they ordered different toppings. Marco’s charges an additional fee for toppings, but all toppings cost the same. Cedric got pepperoni, banana peppers, and black olives on his pizza for a cost of $15.74. Josh ordered mushrooms and eggplant on his pizza and paid $14.49. Using this information, write an equation for the cost of a pizza, C, as a function of the number of toppings, t ordered.

• C = 11.99 + 1.25t

• C = 11.99 - 1.25t

• C = 11.99t + 1.25

• C = 11.99t - 1.25

College tuition at Bedrock University has increased $500 per year for the past six years. Wilma is a freshmen this year and paid $10,250 for her tuition. She is curious about her tuition in the coming years and needs this information as motivation to graduate in four years. Assuming the tuition rate increase remains constant, write an equation to represent the tuition at Bedrock University in x years.

• T = 10,250 + 500t where t is time since your freshmen year

• T = 10,250 - 500t where t is time since your freshmen year

• T = 10,250t + 500 where t is time since your freshmen year

• T = 10,250t - 500 where t is time since your freshmen year

Margaret purchased a new bar of soap. Three days after she originally used the soap, she was curious how much soap per day she was using. She decided to weigh her soap and found that the bar was 103 grams. Four days later she re-measured the same bar of soap and recorded a weight of 80 grams. Assuming that Margaret uses the same amount of soap daily (and that she used the soap daily), write an equation that shows the amount of soap remaining after d days of use.

• S = 120.25 – 5.75d

• S = 120.25 + 5.75d

• S = 120.25d – 5.75

• S = 120.25d + 5.75

A company is selling bubble gum.  The function g(x) = 2x + 4 represents the cost if someone buys x packages of bubble gum.  Find g(8) and explain what it means within the context of the problem.

• g(8) = 2.  This means that after selling 8 packages of gum, the company makes $2.

• g(8) = 2.  This means that the company must sell 2 packages of gum to make $8.

• g(8) = 20.  This means that 8 packages of gum cost $20.

• g(8) = 20.  This means that the company must sell 20 packs of gum to make $8.

The amount of water in a bucket (in pints) can be modeled by the equation f(x) = 2x + 7, where x is the number of pitchers used to fill the bucket.  If the bucket contains 29 pints of water, how many pitchers of water were used to fill it?

Mathematical Equivalence

ON

The amount of water in a bucket (in pints) can be modeled by the equation f(x) = 2x + 7, where x is the number of pitchers used to fill the bucket.  If 8 pitchers were used to fill the bucket, how many pints of water are in the bucket?

Mathematical Equivalence

ON

A company is selling bubble gum.  The function g(x) = 2x + 4 represents the cost if someone buys x packages of bubble gum.  Find x when g(x) = 10 and explain what it means within the context of the problem.

• g(10) = 24.  This means that after selling 10 packs of gum, the company makes $24.

• x = 24 when g(x) = 10.  This means that the company must sell 24 packs of gum to make $10.

• g(10) = 3.  This means that 10 packs of gum cost $3.

• x = 3 when g(x) = 10.  This means that the company must sell 3 packs of gum to make $10.