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?

Tₙ=arⁿ⁻¹

T₅ = 3986

Step-by-step explanation:

In the first year, 1200 people participated.

If the number of residents who will participate is expected to increase by 35% each year,

It means the number of participants next year = 135% of the previous year = 1.35

This us an example of a geometric progression (G. P.) since the next term is gotten from the previous term by multiplication with a common constant 1.35.

The explicit rule that can be used to determine the number of people that will participate at any time is determined by the nth term of a G. P.

Nth term of a G. P., Tₙ=arⁿ⁻¹

Where First term, a = 1200

Common ratio, r = 1.35

Tₙ=arⁿ⁻¹

Tₙ=1200 X 1.35ⁿ⁻¹

In the fifth year,

T₅=1200 X 1.35⁵⁻¹ = 1200 X 1.35⁴ = 3985.8075 = 3986 (to the nearest whole number).

3986 people will participate in the fifth year.