Question

lesson 5 practice problems

1. the cell phone plan from company c costs $10 per month, plus $15 per gigabyte for

data used. the plan from company d costs $80 per month, with unlimited data.
rule c gives the monthly cost, in dollars, of using ( t ) gigabytes of data on company c’s
plan. rule d gives the monthly cost, in dollars, of using ( t ) gigabytes of data on
company d’s plan.
\ta. write a sentence describing the meaning of the statement ( c(2) = 40 ).
\tb. which is less, ( c(4) ) or ( d(4) )? what does this mean for the two phone plans?
\tc. which is less, ( c(5) ) or ( d(5) )? explain how you know.
\td. for what number ( t ) is ( c(t) = 130 )?
\te. draw the graph of each function.
(chart: x-axis: gigabytes of data used, y-axis: dollar cost, grid with 0-8 on x, 0-160 on y)

Explanation:

Part (a)

Step1: Understand the function \( C(t) \)

The function \( C(t) \) represents the monthly cost (in dollars) of using \( t \) gigabytes of data on Company C's plan. The input \( t \) is the amount of data (in gigabytes), and the output \( C(t) \) is the cost (in dollars).

Step2: Interpret \( C(2) = 40 \)

When \( t = 2 \) (meaning 2 gigabytes of data are used), the value of \( C(2) \) is 40. So, this means that using 2 gigabytes of data on Company C's plan costs $40 per month.

Step1: Find the formula for \( C(t) \)

Company C's plan costs $10 per month plus $15 per gigabyte. So, the formula for \( C(t) \) is \( C(t)=10 + 15t \).

Step2: Calculate \( C(4) \)

Substitute \( t = 4 \) into \( C(t) \):
\( C(4)=10+15\times4 = 10 + 60=70 \).

Step3: Find the formula for \( D(t) \)

Company D's plan costs $80 per month with unlimited data. So, \( D(t)=80 \) for any \( t \) (since the cost doesn't depend on data usage).

Step4: Compare \( C(4) \) and \( D(4) \)

\( C(4) = 70 \) and \( D(4)=80 \). Since \( 70<80 \), \( C(4) \) is less than \( D(4) \). This means that for using 4 gigabytes of data, Company C's plan is cheaper than Company D's plan.

Step1: Calculate \( C(5) \)

Using the formula \( C(t)=10 + 15t \), substitute \( t = 5 \):
\( C(5)=10+15\times5=10 + 75 = 85 \).

Step2: Recall \( D(5) \)

Company D's plan is a flat $80 per month, so \( D(5)=80 \).

Step3: Compare \( C(5) \) and \( D(5) \)

Since \( 80<85 \), \( D(5) \) is less than \( C(5) \). We know this because we calculated \( C(5)=85 \) and \( D(5)=80 \), and \( 80 \) is less than \( 85 \).

Answer:

Using 2 gigabytes of data on Company C's plan costs $40 per month.

Part (b)