Expert: Frederick Koh - 2/5/2012

Question
Can you help me with (b) and (c) of this 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
In the 4th year, the price becomes 700+30(4)=820

When 4 < t  9,

P(t)= 820 -30(t-4)= 820 - 30t +120 = 940 - 30t    (shown)

(Note that a time lag factor of t-4 has been installed into the above equation)

In the 9th year, the price becomes 940 - 30( 9)=670

When t> 9,

P(t)= 670 + 15 (t-9) =    535 +15t       (shown)

(Note that a time lag factor of t-9 has been installed into the above equation)


Hope this helps. Peace.