SOLUTION: When a new game system first came out, it cost $500. Over the next couple of years, however, the price fell by 5% each month. Write a function to find the cost, C, after m months.

Question 579226: When a new game system first came out, it cost $500. Over the next couple of years, however, the price fell by 5% each month. Write a function to find the cost, C, after m months.
A)How many months did it take before the price of the game system fell to $200?
B)What was the cost of the game system after 2 years?
SOLVE USING LOGARITHMS(:
Answer by dfrazzetto(283) (Show Source): You can put this solution on YOUR website!

C = 500(1-.05)^n
n=number of months
a)
200 = 500(.95)^n
2/5 = (.95)^n; take log of both sides
log (2/5) = n(log .95)
n = (log 2/5)/(log .95)
n = 17.86 months
b)
n = 24 months
C = 500(.95)^24
C = 500(0.291989024)
C = $146
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