Expert: Paul Klarreich - 2/5/2012

Question
Can you help me with (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
Questioner:Erin
Subject: Piecewise function.

Question:

Can you help me with (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?
P1(t) = 700+30t

>>>>>>>>>>>>  See if you can figure how that was arrived at.  Hint:

It's a straight-line (linear) function, which you can always figure out by
getting:

A) a slope.  (where did that 30 come from?)
B) one point.  Doesn't 'initially' mean t = 0?
.............................

(b) When 4 < t 9 the value of P(t) is given by what part of the piecewise-
defined function?
P2(t) =

>>>>>>>>>>>>  Now do the same.

It's a straight-line (linear) function, which you can always figure out by
getting:

A) a slope.  (What is it between t = 4 and 9?)
B) one point.  What is the price at t = 4?  Doesn't the FIRST function give
you that?  Just apply the first function: P1(4) = ???
Now apply the point-slope form:   P - P1 = m(t - t1), where:

t1 = 4  and P1 = your P1(4)


.......................

(c) When t > 9 the value of P(t) is given by what part of the piecewise-
defined function?
P3(t) =

>>>>>>>>>>  Just keep going.