Question

Ms. Callahan works hard to budget and predict her costs for each month. She is currently attempting to determine how much her cell phone company will likely charge her for the month. She is paying a flat fee of $80 a month for a plan that allows for unlimited calling but costs her an additional twenty cents per text message. a. Write a function, c(t), for Ms. Callahan's current cell plan that will calculate the cost for the month based on the number of text messages she makes. b. Find c(20) d. Find c(t) = 100 c. Find c(45) e. Find c(t) = 90 f. At what number of texts would $20 unlimited texting be less expensive then her current plan?

Answer 1

The function is

$c(t)=80+0.2t$

since she pays $80 flat, and then $0.2 for each text message.

This implies that

$c(20)=80+0.2\cdot 20 = 80+4=84$

$c(t)=100\iff 80+0.2t=100 \iff 0.2t = 20 \iff t=\dfrac{20}{0.2}=100$

$c(45)=80+0.2\cdot 45 = 80+9=89$

$c(t)=90\iff 80+0.2t=90\iff 0.2t = 10 \iff t=\dfrac{10}{0.2}=50$

For the last question, we have to see how many texts it takes to pay $20: we have

$0.2t=20 \iff t=\dfrac{20}{0.2}=100$

So, if she sends less than 100 texts a month, it is more convenient to pay $0.2 for each text. If the sends more than 100 texts a month, it is more convenient to pay a flat fee of $20 for unlimited messages.