We have been given that a limited edition poster increases in value each year with an initial value of $18. After one year and an increase of 15% per year, the poster is worth $20.70.
We will use exponential growth formula to find our required equation.
We know that an exponential function is in form [tex]y=a\cdot (1+r)^x[/tex], where
a = Initial value,
r = Growth rate in decimal form,
x = Time.
Let us convert 15% into percentage.
[tex]15\%=\frac{15}{100}=0.15[/tex]
Initial value is 18.
Upon substituting these values in above formula, we will get:
[tex]y=18(1+0.15)^x[/tex]
[tex]y=18(1.15)^x[/tex]
Let us check our function by finding the value of poster after one year as:
[tex]y=18(1.15)^1[/tex]
[tex]y=18(1.15)[/tex]
[tex]y=20.70[/tex]
Since the value of poster after 1 year matched with our findings, therefore, the equation [tex]y=18(1.15)^x[/tex]can be used to fund the value, y, after x years.
