Question

question 19
4 pts
amdm.par.8.1 (mc)
given this exponential function rule,
identify the recursive rule:
$y_0 = 15; y_{n+1} = y_n \times 47$

$\bigcirc y_{n+1} = 15 \times 47^{n-1}$

$\bigcirc y_n = 47 \times 15^n$

$\bigcirc y_n = 15 \times n^{89}$

$\bigcirc y_n = 15 \times 47^n$

Explanation:

Step1: Expand recursive rule

Calculate initial terms:
$Y_0 = 15$
$Y_1 = Y_0 \times 47 = 15 \times 47$
$Y_2 = Y_1 \times 47 = 15 \times 47 \times 47 = 15 \times 47^2$
$Y_3 = Y_2 \times 47 = 15 \times 47^3$

Step2: Generalize explicit form

From the pattern, for any $n$, $Y_n = 15 \times 47^n$

Step3: Verify options

Match the generalized form to the choices.

Answer:

$Y_n = 15 \times 47^n$