Question

question 18
4 pts
amdm.par.8.1 (mc)
which of the following is an exponential function rule for this sequence:
(4,12,36,108,324)

$y_n = 4 \times 3^{n - 1}$

$y_{n + 1} = y_n \times 3$

$y_n = 3 \times 2^n$

$y_{n + 1} = y_n \times 2$

Explanation:

Step1: Identify sequence type

This is a geometric sequence (each term is multiplied by a constant to get the next term). The common ratio $r = \frac{12}{4} = 3$, and the first term $a_1 = 4$.

Step2: Recall geometric sequence formula

The explicit (exponential) function rule for a geometric sequence is $Y_n = a_1 \times r^{n-1}$.

Step3: Substitute values

Substitute $a_1=4$ and $r=3$ into the formula: $Y_n = 4 \times 3^{n-1}$.

Step4: Verify with terms

For $n=1$: $Y_1=4 \times 3^{0}=4$; $n=2$: $Y_2=4 \times 3^{1}=12$; $n=3$: $Y_3=4 \times 3^{2}=36$, which matches the given sequence. The other options either are recursive rules or do not generate the sequence.

Answer:

$Y_n = 4 \times 3^{n-1}$