Question

The function y= 25• 2^x models the jackpot y, in dollars, in the game show for x weeks. Write a recursive formula.

Answer 1

The recursive formula would be


`g_n=g_(n-1)* 2`.

The explicit formula given is in the form


`g_n=g_1 * r^(n-1)`

We can manipulate this formula to find the initial value as well as the growth rate:


`g_n=g_1 * r^(n-1) = g_1 * r^n * r^(-1) \\ \\=g_1 * r^n * (1)/(r) \\ \\=g_1 * (1)/(r) * r^n= (g_1)/(r)* r^n`

Viewing our equation in this form, we know that

`(g_1)/(r) = 25 \\ \\\text{ and } r=2`

which tells us that g₁ = 50.

Since r = 2, we can write our recursive formula:


`g_n=g_(n-1)* 2`