Question

PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!

When the town of Samuel Village first started its voluntary recycling program, 1200 of the town’s residence participated. The town predicts that the number of people participating in the recycling program will increase by 35% each year.

Which explicit rule can be used to determine the number of people participating in the program in the fifth year?

Answer 1

`a_n = 1200(1.35)^n`

Explanation:

Equation to remember:

`P_0(1+r)^t` where t = time

`P_0` = 1200 since that's the initial population

`r` = .35 rate of change \\

`t` = 5 years

Plug in the numbers;

`a_5 = 1200(1+.35)^5`

Since the prompt looks like it's asking for an equation given any number of years.. then just change 5 to n for number of years.

`a_n = 1200(1.35)^n`

Answer 2

Answer:
`\bold{(A)\ a_n=1200(1.35)^(n-1)}`

Explanation:

The explicit rule for a geometric sequence is:
`a_n=a_1(r)^(n-1)\quad \text{where}\ a_1\ \text{is the first term and r is the ratio}`

The sequence starts at 1200, so
`a_1` = 1200.

The rate increases 35% so r = 1.35

`a_n=a_1(r)^(n-1)\\.\quad=1200(1.35)^(n-1)\\\\a_5=1200(1.35)^(5-1)\\.\quad=1200(1.35)^4`