Another question:
A cell phone company charges $60 for a cell phone and $40 per month under its economy plan. Formulate and graph a model that can be used to determine the total cost, C(t), of operating a cell phone for t months. Find the total cost for 5 and 1/2 months of service and the domain of C.
I understand everything except how you would find the domain of C. Please walk me through it so I can apply it to other problems. Thank you so much!
did you have C(t) = 40t + 60 ?
now the graph would only make physical sense for the part in the first quadrant.
the y-intercept is the point (0,60), (even with no calls you would pay $60)
the graph would continue to rise as t increases.
so the lowest Cost is 60 and there is really no upper limit, but we have to be reasonable about large values of t
e.g. if t = 1000, this would make no sense because 1000 months from now, cells phones may only be found in museums.
I would say the domain of t is any reasonable value of t , t > 0
you said "domain of C", what you meant is the range of C
domain deals with the horizontal variable,
range deals with the vertical variable of your function.
That's funny, because in my packet, it said to "find the domain of C." But I see how that would not make sense.
Thanks!
To find the domain of C, we need to consider the constraints or limitations on the variable t. In this case, t represents the number of months of service.
Since it wouldn't make sense to have a negative or zero number of months for the service, the domain would exclude any values less than or equal to zero. Additionally, we need to consider if there is any practical or maximum limit on the number of months for the service. In this problem, we don't have any specific information about a maximum limit on the number of months.
Therefore, the domain of C would be any positive real numbers, excluding zero. In interval notation, the domain would be (0, +∞). This means that any positive number of months can be plugged into the model to calculate the total cost.
To recap, the domain of C in this problem is (0, +∞), which means any positive real number of months can be used as input to find the total cost of operating a cell phone.