Expert: Scotto - 2/5/2012

Question
Can you help me with parts (b) and (c) of the following question?

The price of an item is initially $700. For the first 4 years the price increases by $30 each year. For the next 5 years the price decreases by $30 per year. From then on the price increases by $15 per year. Find a piecewise-defined function P that specifies the price of the item after t years have passed. Let P(t) = the price of the item in dollars after t years have passed. (Note: Do not use $ signs within your answers.)
(a) When 0 < t 4, the value of P(t) is given by what part of the piecewise-definedfunction?
P(t) = 700+30t

(b) When 4 < t 9 the value of P(t) is given by what part of the piecewise-defined function?
P(t) =

(c) When t > 9 the value of P(t) is given by what part of the piecewise-defined function?
P(t) =


Thanks in advance!!!

Answer
a) After 4 years, the value will have gone up by $120, so it will be worth $820.
To get an equation, just take that value and subtract of $30 times the years.
Here, t would be 0, 1, 2, 3, or 4, and the answer is correct: P(t) = 700 + 30t.

For the next 5 years, we subtract $30 per year, so it would be $820 - 15(t-4).
Here, t would be 4, 5, 6, 7, 8, or 9.

Since it went up for 4 years at $30 per year and down by $30 for the next five years,
that means it went down by one more year than it went up.
This means at the end of year 9 the value is $30 less than the original.
Since it increase by $15 per year, we just need to take that price plus $15(n-9) to get the price after 9 years.