Media services charges $40 for a phone and 20/mth for its economy plan. It says to find a model that determines the total cost, C(t), of operationg a media Services phone for t months. I think the answer should be in this equation - y = mx+b. Not sure.
Algebra/Equations,functions - MathMate, Friday, November 26, 2010 at 11:34am
So far so good.
What values would you assign to m and b to complete the operation model?
Algebra/Equations,functions - AMY, Friday, November 26, 2010 at 12:47pm
y = 40x+20?
Algebra/Equations,functions - MathMate, Friday, November 26, 2010 at 1:33pm
Correct!
Algebra/Equations,functions - MathMate, Friday, November 26, 2010 at 1:35pm
Watch out, it's $20/month and the phone (one time only) is $40.
so the equation should be:....
Algebra/Equations,functions - AMY, Friday, November 26, 2010 at 5:19pm
not sure but will take a stab at it. y = 20x +40?
Algebra/Equations,functions - AMY, Friday, November 26, 2010 at 6:44pm
Nope that was wrong on my part. I believe the final answer is C(t) = 20t+40
Algebra/Equations,functions - AMY, Friday, November 26, 2010 at 7:55pm
I also need to find the total cost. This is what I have.
C = 20(0) +40. (0,40).
C (5) = 20 (5) + 40.
C (5) = 100 +40 = 140 (5, 140)
So the total cost is 130. IS THIS RIGHT? Thank you!
Thank you for the follow-up. Sorry that I didn't check your responses.
Yes, in a function, we normally assume that
C(x)=ax+b
is equivalent to
C(t)=at+b
because t is a "dummy" variable.
However in your case, t has been stated as the variable, so it is more correct to define function as:
C(t)=20t+40
Hope you understood fully why $20 per month is associated with the variable t.
Yes. DId you see the total cost?? Was I right with the answer to that one? I think I was right.
No, I didn't.
But if total cost for t months,
C(t) = 20t + 40, then
For 0 month:
C(0) = 20(0)+40 = 40
for 4 months:
C(4) = 20(4)+40 = 120
for 5 months:
C(5) = 20(5)+40 = 140
I do not understand how you get 130 (for 5 months)!
The question has not stipulated for how many months the total cost should be calculated.
To find the model that determines the total cost of operating a Media Services phone for t months, you will need to use the equation y = mx + b, where y represents the total cost, x represents the number of months (t), m represents the rate per month, and b represents the initial cost (phone cost).
In this case, the phone cost is $40, which is a one-time only cost and does not change with time. Therefore, b = 40.
The monthly cost for the economy plan is $20, and it remains constant throughout the months. So, the rate per month is m = 20.
Substituting these values into the equation, you get y = 20x + 40. This equation represents the model for the total cost (y) of operating a Media Services phone for t months (x).
For example, if you want to find the total cost after 5 months (x = 5), you substitute x=5 into the equation:
y = 20(5) + 40
= 100 + 40
= 140
Therefore, the total cost after 5 months would be $140 (y = 140).
So, your final answer for the model that determines the total cost of operating a Media Services phone for t months is C(t) = 20t + 40, where C(t) represents the total cost after t months.