Question

The weekly cost of food for a family of four using the moderate cost plan in the United States increased at a relatively constant rate of $4.83 per year from 1997 to 2004. In 2004, the weekly cost of food for a family of four was $186.90. a. What was the weekly cost of food for a family of four in 1997? b. Write an equation that gives the weekly cost of food for a family of four as a function of the number of years since 1997. c. Find the weekly cost of food for a family of four in 2010 assuming the same rate of increase.

Answer 1

Answer:

Part a) The weekly cost of food for a family of four in 1997 was $153.09

Part b) $y=4.83x+153.09$

Part c) $\ 215.88$

Step-by-step explanation:

Part a. What was the weekly cost of food for a family of four in 1997?

Let

y ---->the weekly cost of food for a family of four

x ---> the number of years since 1997

we know that

The linear equation in point slope form is equal to

$y-y1=m(x-x1)$

In this problem we have a linear function between variable x and variable y

In 2004, the weekly cost of food for a family of four was $186.90

so

In the year 2004

The value of x is equal to

x=2004-1997=7 years

we have

$point\ (7,186.90)$

$m=\ 4.83\ per\ year$

substitute

$y-186.90=4.83(x-7)$ ----> equation in point slope form

Remember that the year 1997 is when the value of x is equal to zero

so

For x=0

$y-186.90=4.83(0-7)$

solve for y

$y=4.83(-7)+186.90$

$y=153.09$ -----> y-intercept or initial value

therefore

The weekly cost of food for a family of four in 1997 was $153.09

Part b. Write an equation that gives the weekly cost of food for a family of four as a function of the number of years since 1997

we know that

The linear equation in slope intercept form is equal to

$y=mx+b$

where

m is the slope

b is the y-intercept or initial value

we have

$m=\ 4.83\ per\ year$

$b=\ 153.09$ ----> initial value in 1997

substitute

$y=4.83x+153.09$

Part c. Find the weekly cost of food for a family of four in 2010 assuming the same rate of increase

In the year 2010

x=2010-1997=13 years

substitute in the linear equation

$y=4.83(13)+153.09=215.88$