Answer:
[tex]f(n) = 3T_{n-1}[/tex]; [tex]T_1 = 12[/tex]
Step-by-step explanation:
Given
[tex]f(x) = 4*3^x[/tex]
Required
Write as a recursive function
Substitute 1 for x.
[tex]f(1) = 4*3^1 = 4 * 3 = 12[/tex]
[tex]f(2) = 4*3^2 = 4 * 9 = 36 = 12 * 3[/tex]
[tex]f(3) = 4*3^3 = 4 * 27 = 108 = 36 * 3[/tex]
Following the above pattern:
[tex]f(n) = T_{n-1} * 3[/tex]
[tex]f(n) = 3T_{n-1}[/tex]
Hence, the recursive function is:
[tex]f(n) = 3T_{n-1}[/tex]; [tex]T_1 = 12[/tex]
