When the town of Manning first started its voluntary recycling program, 2500 of the town’s residence participated. The town predicts that the number of people participating in the recycling program will increase by 5% each year.
Which explicit rule can be used to determine the number of people participating in the program in the fifth year?
I have trouble understanding these so if you could explain how you did it that would be much appreciated.
Note : Here....I'm assuming that "in the fifth year" means "after five years"
an = Final number
2500 = Starting number
Growth rate (express as a decimal ) = 5% = .05
n = number of years
Final number = Starting number ( 1 + growth rate)^n
an = 2500 (1 + .05)^n (simplify)
an = 2500 (1.05)^n
Okay thanks you for showing me how you did it. It helped me understand the problem better.
I tried that answer and I got it inccorect. Could you explain how it was wrong?
OK....I see what they are assuming...
They are assuming that during the 1st year, we have 2500
So...."in the 5th year" means "after 4 years"
So....in that case
2500 (1.05)^(n - 1) is correct.... !!!