Answer:
(a) [tex]f(x)=3500(\frac{2}{\sqrt{7}})^x[/tex]
(b) $245.27
Explanation:
(a)
From the below graph it is clear that the graph it passes through the points (0,3500) and (2,2000).
The general form of an exponential function is
[tex]f(x)=ab^x[/tex]
where, a is the initial value and b is growth or decay factor.
Initial value is 3500, it means a=3500.
[tex]f(x)=3500b^x[/tex]
f(x)=2000 at x=2.
[tex]2000=3500b^2[/tex]
[tex]\frac{2000}{3500}=b^2[/tex]
[tex]\frac{4}{7}=b^2[/tex]
[tex]\sqrt{\frac{4}{7}}=b[/tex]
[tex]\frac{2}{\sqrt{7}}=b[/tex]
The exponential function for the graph is
[tex]f(x)=3500(\frac{2}{\sqrt{7}})^x[/tex]
(b)
We need to find the value of the boat after 9.5 years.
Substitute x=9.5 in the above function.
[tex]f(9.5)=3500(\frac{2}{\sqrt{7}})^{9.5}[/tex]
[tex]f(9.5)=245.26598[/tex]
[tex]f(9.5)\approx 245.27[/tex]
Therefore, the value of the boat after 9.5 years is $245.27.
