Question

The current cost of a hamburger is $4.00, but it is increasing by 9% each year. Write the exponential function that model this situation. How much will the hamburger cost in two years? How much will it cost in four years and six months from now?

Answer 1

Part a)
`y=4(1.09)^x`

Part b)
`\$4.75`

Part c)
`\$5.89`

Explanation:

Part a) Write the exponential function that model this situation

we know that

In a exponential function of the form

`y=a(b)^x`

a is the initial value or the y-intercept

b is the base of the exponential function

If b > 1 we have a exponential growth function

If b < 1 we have a exponential decay function

r is the percentage rate of change

b=(1+r)

In this problem we have

x ----> the number of years

y ----> the cost of a hamburger

`a=\$4`

`r=\%9=9/100=0.09`

`b=1+r=1+0.09=1.09`

substitute the values

`y=4(1.09)^x` ----> exponential growth function

Part b) How much will the hamburger cost in two years?

For x=2 years

substitute

`y=4(1.09)^2`

`y=\$4.75`

Part c) How much will it cost in four years and six months from now?

Remember that

`1\ year=12\ months`

so

four years and six months is equal to 4.5 years

For x=4.5 years

substitute

`y=4(1.09)^4.5`

`y=\$5.89`