ANSWER
[tex]\begin{gathered} a_n=ar^{n\text{ - 1}} \\ a_8\text{ = \$38.26} \end{gathered}[/tex]
EXPLANATION
The problem represents a geometric progression.
The general form of a geometric sequence is:
[tex]a_n=ar^{n\text{ - 1}}[/tex]
where a = first term
r = common ratio
The first term from the table is the first price (for the first month). That is $80.00
To find the common ratio, we divide a term by its preceeding term.
Let us divide the price of the second month from the first.
We have:
[tex]\begin{gathered} r\text{ = }\frac{72}{80} \\ r\text{ = 0.9} \end{gathered}[/tex]
The price after the 8th month is the value of a(n) when n = 8
So, we have that:
[tex]\begin{gathered} a_8\text{ = 80 }\cdot0.9^{(8\text{ - 1)}} \\ a_8\text{ = 80 }\cdot0.9^7 \\ a_8\text{ = \$38.26} \end{gathered}[/tex]
