Question

The function f(x) = 4 x 3^x models the population of tadpoles in a frog pond after x years. Write a recursive formula to model the situation

Answer 1

`f(n) = 3T_(n-1)`;
`T_1 = 12`

Explanation:

Given

`f(x) = 4*3^x`

Required

Write as a recursive function

Substitute 1 for x.

`f(1) = 4*3^1 = 4 * 3 = 12`

`f(2) = 4*3^2 = 4 * 9 = 36 = 12 * 3`

`f(3) = 4*3^3 = 4 * 27 = 108 = 36 * 3`

Following the above pattern:

`f(n) = T_(n-1) * 3`

`f(n) = 3T_(n-1)`

Hence, the recursive function is:

`f(n) = 3T_(n-1)`;
`T_1 = 12`