Question

A can of soda in 1972 costs $0.12, by 2012 it cost $1.35.Find the rate at which the cost of a can of soda increases over this time period.Construct a linear model that can be used to predict the cost of soda.Use your linear model to predict the cost of soda in 2016.

Answer 1

We can use a linear model so it will be in the form

y = mx+b where m is the slope and b is the y intercept

We have two points on the line

Letting 1972 be year 0 then 2012 is 2012-1972 = 40 or 40 years later

( 0 , .12) and ( 40, 1.35)

We can find the slope

m = ( y2-y1)/(x2-x1)

= ( 1.35 -.12)/ (40-0)

=1.23/40

=.03075

Rate of increase = .03075 cents per year

=.031 cents per year rounded to the thousandths place

y = .031x +b

We can use the first point to help us find b

When the value of x is zero, the the value of y is the y intercept

y = .031x + .12

We can find the value in 2016

2016- 1972 = 44 years

y = .031(44) +.12

y =1.364+.12

y = 1.484

Rounding to the nearest cent

y = 1.48