Question 1183107
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.