Answer:
[tex]f(4) = 1280[/tex]
Step-by-step explanation:
Given
[tex]f(1)= 160[/tex]
[tex]f(n+1) = 2f(n)[/tex]
Required
Determine f(4)
Take n as 3:
[tex]f(n+1) = 2f(n)[/tex] becomes
[tex]f(3+1) = 2f(3)[/tex]
[tex]f(4) = 2f(3)[/tex]
We need to get f(3).
Take n as 2
[tex]f(n+1) = 2f(n)[/tex] becomes
[tex]f(2+1) = 2f(2)[/tex]
[tex]f(3) = 2f(2)[/tex]
We need to get f(2).
Take n as 1
[tex]f(n+1) = 2f(n)[/tex] becomes
[tex]f(1+1) = 2f(1)[/tex]
[tex]f(2) = 2f(1)[/tex]
Substitute 160 for f(1)
[tex]f(2) = 2 * 160[/tex]
[tex]f(2) = 320[/tex]
Recall that:
[tex]f(3) = 2f(2)[/tex]
[tex]f(3) = 2 * 320[/tex]
[tex]f(3) = 640[/tex]
Recall that:
[tex]f(4) = 2f(3)[/tex]
[tex]f(4) = 2 * 640[/tex]
[tex]f(4) = 1280[/tex]
