Answer:
General form of an exponential equation: [tex]y=ab^x[/tex]
where:
Let x = years
Let y = investment value
Use (2, 692) and (4, 952) to find a and b of the exponential equation:
[tex]ab^2=692[/tex]
[tex]ab^4=952[/tex]
[tex]\implies \dfrac{ab^4}{ab^2}=\dfrac{952}{692}[/tex]
[tex]\implies b^2=\dfrac{238}{173}[/tex]
[tex]\implies b=\sqrt{\dfrac{238}{173}}=1.17\:\textsf{(nearest hundredth)}[/tex]
[tex]\implies ab^2=a\left(\dfrac{238}{173}\right)=692[/tex]
[tex]\implies a=\left(\dfrac{59858}{119}\right)=503.01\:\textsf{(nearest hundredth)}[/tex]
Therefore, the exponential equation is:
[tex]y=503.01(1.17)^x[/tex]
18 years after the initial investment is when [tex]x=18[/tex]:
[tex]\implies 503.01(1.17)^{18}=8490[/tex]
Therefore, the amount closest to the value of the investment 18 years after the initial investment is $8490
(If you use the exact values for a and b rather than the rounded values, the amount is $8879)
