Answer:
The solution tells me that in 124.5 years the value of the dollar in both investments will be the same
Step-by-step explanation:
Let
t ----> the number of years
f(t) ---> the dollar value of one investment
g(t) ---> the dollar value of the other investment
we have
[tex]f(t)=1,800(1.055)^t[/tex]
[tex]g(t)=9,500(1.041)^t[/tex]
Solve the equation f(t)=g(t)
[tex]9,500(1.041)^t=1,800(1.055)^t[/tex]
[tex]\frac{9,500}{1,800}=\frac{(1.055)^t}{(1.041)^t}[/tex]
Rewrite
[tex]\frac{9,500}{1,800}=(\frac{1.055}{1.041})^t[/tex]
Apply log both sides
[tex]log(\frac{9,500}{1,800})=log(\frac{1.055}{1.041})^t[/tex]
[tex]log(\frac{9,500}{1,800})=tlog(\frac{1.055}{1.041})[/tex]
[tex]t=log(\frac{9,500}{1,800})/log(\frac{1.055}{1.041})[/tex]
[tex]t=124.5\ years[/tex]
therefore
The solution tells me that in 124.5 years the value of the dollar in both investments will be the same
