Question

16) The price of tea cooler has increased linearly since 2010. In 2013 the price for a gallon was $2.05. In 2018 the price was $2.65. a) Find m. What does this number represent? b) Find b. What does this number represent? c) How much will a gallon of tea cooler cost in 2022?

Answer 1

16. The linear function is given by

P = mx + b

where P is the price of the tea cooler after x years since 2010

For the year 2013, x = 2013 - 2010 = 3 years

Given, when x = 3, P = $2.05

Therefore,

2.05 = m(3) + b

=> b = 2.05 - 3m ------------(i)

For the year 2018, x = 2018 - 2010 = 8 years

Given, when x = 8, P = $2.65

Therefore,

2.65 = m(8) + b

=> 2.65 = 8m + 2.05 - 3m

=> 5m = 2.65 - 2.05

=> 5m = 0.60

=> m = 0.12

Substituting the value of m in (i) we get

b = 2.05 - 3(0.12) = 2.05 - 0.36 = 1.69

=> b = 1.69

Therefore,

P = 0.12x + 1.69

a) m = 0.12

This number represents the slope i.e. the price for a gallon of tea cooler increases by $0.12 each year

b) b = 1.69

This number represents the price of tea cooler in 2010

c) For the year 2022, x = 2022 - 2010 = 12 years

Substituting x = 12 we get

Price of tea cooler in 2022

= 0.12(12) + 1.69

= 1.44 + 1.69

= $3.13