Question 1183107: Starting in the year 2012, the number of speeding tickets issued each year in Middletown is predicted to grow according to an exponential growth model. During the year 2012, Middletown issued 150 speeding tickets (P0=150). Every year thereafter, the number of speeding tickets issued is predicted to grow by 5%.
If Pn denotes the predicted number of speeding tickets during the year 2012+n, then
Write the recursive formula for Pn
Pn = ×Pn−1
Write the explicit formula for Pn
Pn =
If this trend continues, how many speeding tickets are predicted to be issued in 2028?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the exponential formula is:
y = a * b ^ x
if you let y = Pn and a = P0 and b = x and x = n, the formula becomes:
Pn = P0 * x ^ n
if you let P0 = 150 and x = 1.05, the formula becomes:
Pn = 150 * 1.05 ^ n
that's the explicit formula.
the recursive formula will be:
Pn = Pn-1 * 1.05
2012 is the start year.
in that year, n = 0
2028 is the year you want to project to.
in that year, n = 2028 - 2012 = 16
P16 = P0 * 1.05 ^ 16 gets you the value in 2028 directly from the value in 2012.
when P0 = 150, the formula becomes:
P16 = 150 * 1.05 ^ 16 = 327.4311883
the recursive formula will get you that value from the value in P15.
the formula for the value in P15 is:
P15 = 150 * 1.05 ^ 15 = 311.8392269
the recursive formula is Pn = Pn-1 * 1.05
when n = 16, the formula becomes:
P16 = P15 * 1.05
when the value in P15 is 311.8392269, the formula becomes:
P16 = 311.8392269 * 1.05 = 327.4311883.
using the recursive formula, you need to know the value in Pn-1 so that you can find the value in Pn.
using the explicit formula, you can find the value in Pn directly from the value in P0.
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