(Solution) - Text Time charges 25 for a texting plan with 300 text -(2025 Original AI-Free Solution)

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Academic Level: Undergrad. (yrs 3-4)

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Text-Time charges $25 for a texting plan with 300 text messages included. If the customer goes over the 300 messages, the cost is $0.10 per message. They have an unlimited plan for $48 per month.
a. If x represents the number of text messages, and c(x) represents the cost of the messages, express c(x) as a piecewise function.
b. Graph the function from part a.
c. What are the coordinates of the cusp in your graph from part b?
d. On the same axes as your graph from part b, graph the function c(x) = 48, which represents the cost under the unlimited plan.
e. For what number of text messages are the costs of the two different plans the same?