Answer:
Part a) [tex]y=4(1.09)^x[/tex]
Part b) [tex]\$4.75[/tex]
Part c) [tex]\$5.89[/tex]
Step-by-step explanation:
Part a) Write the exponential function that model this situation
we know that
In a exponential function of the form
[tex]y=a(b)^x[/tex]
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
[tex]a=\$4[/tex]
[tex]r=\%9=9/100=0.09[/tex]
[tex]b=1+r=1+0.09=1.09[/tex]
substitute the values
[tex]y=4(1.09)^x[/tex] ----> exponential growth function
Part b) How much will the hamburger cost in two years?
For x=2 years
substitute
[tex]y=4(1.09)^2[/tex]
[tex]y=\$4.75[/tex]
Part c) How much will it cost in four years and six months from now?
Remember that
[tex]1\ year=12\ months[/tex]
so
four years and six months is equal to 4.5 years
For x=4.5 years
substitute
[tex]y=4(1.09)^4.5[/tex]
[tex]y=\$5.89[/tex]
