Piecewise Functions...

Question

Lucinda’s cell phone plan includes 8GB of data and costs $35 each month. If she uses more than 8GB of data, the company charges her $10 per additional GB. Let 𝑃(𝑑) be a function that describes how much Lucinda pays at the end of the month if she uses 𝑑 GB of data.

a. Find and interpret P(8.5)

b. Write P(d) as a piecewise function (including the "P(d)=" part)

Answer 1

I will model this for you assuming 6 GB, $ 40 , and $ 15 per additional gb over 6 (your numbers are 8, 35, 10).

P (8.5) is the amount she pays if she uses 8.5 GB of data in a month.

Calculating it

Fixed cost $ 35

First 6 GB of data - no extra cost

Remaining 2.5 GB, $ 15 per GB, so cost = 2.5 x 15

So p(8.5) = 35 + 0 + 2.5 x 15 = 72.5

(b) If d <= 6, p(d) = 35 (fixed cost, no extra data charge)

if d >6 p(d) = 35 + 15 (d-6) (fixed cost plus extra charge per GB over 6)

so p(8.5) = 35 + 15 (8.5 - 6) = 72.5 as above

So now write out your solution, using my model and your numbers

Mike