SOLUTION: Problem2. High Tech Graphics bought a fax machine for $750. The fax machine depreciates at a rate of $25 a month. (a) Find a function F that can be used to determine the value of

Algebra ->  Graphs -> SOLUTION: Problem2. High Tech Graphics bought a fax machine for $750. The fax machine depreciates at a rate of $25 a month. (a) Find a function F that can be used to determine the value of      Log On


   

Question 201383: Problem2.
High Tech Graphics bought a fax machine for $750. The fax machine depreciates at a rate of $25 a month.
(a) Find a function F that can be used to determine the value of the fax machine t months after purchase.

F(t)=?

b) I need a graph of the function F(t)?

Thank you so much!!!!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let
x=time in months (ie t=0 means 0 months, t=1 means 1 month)
y=value of the machine



At first, the machine is $750. So at time x=0 the value of the machine is $750 which means that y=750. So we have one ordered pair (ie point) that is (0, 750).

After one month, the machine has lost $25 of its value. So after one month, the value of the machine is now $750-$25=$725 giving the values x=1 and y=725. So we have another ordered pair (point) of (1, 725)


a)

Now that we have two points (0, 750) and (1, 725), we can find the equation of the line that goes through them.

First let's find the slope of the line through the points and


Note: is the first point and is the second point .


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula.


m=%28725-750%29%2F%281-0%29 Plug in y%5B2%5D=725, y%5B1%5D=750, x%5B2%5D=1, and x%5B1%5D=0


m=%28-25%29%2F%281-0%29 Subtract 750 from 725 to get -25


m=%28-25%29%2F%281%29 Subtract 0 from 1 to get 1


m=-25 Reduce


So the slope of the line that goes through the points and is m=-25


Now let's use the point slope formula:


y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula


y-750=-25%28x-0%29 Plug in m=-25, x%5B1%5D=0, and y%5B1%5D=750


y-750=-25x-25%280%29 Distribute


y-750=-25x%2B0 Multiply


y=-25x%2B0%2B750 Add 750 to both sides.


y=-25x%2B750 Combine like terms.



So the equation that goes through the points and is y=-25x%2B750

Now replace the "y" with F(t) and the "x" with "t" to get the function F%28t%29=-25t%2B750


==========================================

Answer:


So the function F that models the value of the fax machine is F%28t%29=-25t%2B750





b)

To graph ANY linear function, simply plot two points and draw a line through them (it's that simple). Since we already know that the function goes through the points (0, 750) and (1, 725), just plot these points and draw a line through them like so:





Note: the ticks on the x-axis are one unit apart. The x-axis is so far down below that it can't be shown (without distorting the graph).