Answer:
4.4 years
Step-by-step explanation:
we know that
The equation of a exponential decay function is given by
[tex]y=a(1-r)^x[/tex]
where
a is the initial value
r is the rate of change
The equation of a exponential growth function is given by
[tex]y=a(1+r)^x[/tex]
where
a is the initial value
r is the rate of change
step 1
Find f(x)
in this problem we have
[tex]f(x)=1,000(1-0.05)^x[/tex]
[tex]f(x)=1,000(0.95)^x[/tex]
step 2
Find g(x)
in this problem we have
[tex]g(x)=400(1+0.17)^x[/tex]
[tex]g(x)=400(1.17)^x[/tex]
step 3
we have
[tex]f(x)=1,000(0.95)^x[/tex]
[tex]g(x)=400(1.17)^x[/tex]
[tex]f(x)=g(x)[/tex]
solve the system by graphing
The solution is the x-coordinate of intersection point
using a graphing tool
The solution is x=4.4 years
see the attached figure
