Answer: 2005
Step-by-step explanation:
Exponential function to determine the value of item after t years,
[tex]f(x)=A(1+r)^t[/tex] , where r= rate of growth, A=Initial value.
As per given , A = 7.85% = 0.0785
A = $125,000
Substitute all values in function, we get
[tex]f(x)=125000(1+0.785)^t[/tex]
When f(x)= 3A , then
[tex]3A=A(1.0785)^t\\\\\Rightarrow\ 3=(1.0785)^t[/tex]
Taking tog on both sides , we get
[tex]\ln 3=t\ln 1.0785\\\\\Rightarrow\ t=\dfrac{\ln 3}{\ln 1.0785}\\\\\Rightarrow t=\dfrac{1.09861228867}{0.0755711868471}\approx15[/tex]
The year will be 1990+15= 2005
Hence, the required year = 2005
