help me i am so lost

Question

math problem The phone company calculates a customer’s monthly cell phone bill as follows: monthly service charge: $35 voice charges: First 100 minutes: $0.018 per minute Second 100 minutes: $0.034 per minute Additional minutes: $0.055 per minute

a. What is the charge for a month in which 158 minutes were used?
b. What is the charge for a month in which 311 minutes were used?
c. Construct a piecewise function that gives the monthly charge for x minutes of usage.

Answer 1

a. What is the charge for a month in which 158 minutes were used?

 

fix charge=monthly service charge=35

First 100 minutes: $0.018 per minute=1.8

next 58 minutes=58*0.034=1.972

 

charge for a month in which 158 minutes were used=35+1.8+1.972=$38.772

 

b. What is the charge for a month in which 311 minutes were used?

 

fix charge=monthly service charge=35
First 100 minutes: $0.018 per minute=1.8
next 100 minutes=$0.034 per minute=3.4

next 111 minues:$0.055 per minute=6.105

 

charge for a month in which 311 minutes were used= 35+1.8+3.4+6.105=$46.305

 

 

 

 

Answer 2

A piecewise function changes the function evaluation rule depending on the x-value being considered.

So, let’s construction the function (for c), then evaluate it for (a) and (b).

Note: all values are for a monthly bill.

A. There is a monthly service charge of $35 no matter how many minutes are used.
      Y = $35 + ???

B. $0.018 per minute for first 100 minutes
      Y = $35 + $0.018x for 0 <= x <= 100

C. $0.034 per minute for second 100 minutes
      Y = $35 + $1.80 + $0.035*(x-100) for 100 < x <= 200

D. $0.055 per minute for each additional minute
      Y = $35 + $1,80 + $3.50 + $0.055*(x-200) for 200 < x

Now, for answer (c):
      Y = $35 + $0.018x for 0 <= x <= 100
      Y = $35 + $1.80 + $0.035*(x-100) for 100 < x <= 200
      Y = $35 + $1,80 + $3.40 + $0.055*(x-200) for 200 < x

(a) For 158 minutes, use the second line:
      Y = $35 + $1.80 + $0.035*(x-100) for 100 < x <= 200
      Y = $35 + $1.80 + $0.035*(58) [you can calculate this]

(b) for 311 minutes, use the third line:
      Y = $35 + $1,80 + $3.40 + $0.055*(x-200) for 200 < x
      Y = $35 + $1.80 + $3.40 + $0.055*(111) [you can calculate this, too]