5 When the town of Samuel Village first started its voluntar

5.

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?

an=1200(0.35)^n

an=1200(0.35)^n1

an=1200(1.35)^n

an=1200(1.35)^n1

Solution

According to the given question

a = 1200

and d = 35% increase in 1200 every year = 1200 x 35/100 = 420 (first year)

d₂ = 1620 x 35/100 =567 (2nd year)

d_n = 1200{(1+35/100)ⁿ-1} = 1200{(1.35)ⁿ - 1}

Hence the explicit rule that can be used to determine the number of people participating in the program in the fifth year will be

a_n = 1200(1.35)ⁿ1