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.

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

Part b)

Part c)

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

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

substitute

----> equation in point slope form

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

so

For x=0

solve for y

-----> 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

where

m is the slope

b is the y-intercept or initial value

we have

----> initial value in 1997

substitute

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

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