Question

let c be the function whose graph is given to the right. this graph represents the cost c of using m anytime cell phone minutes in a month for a five - person family plan.
(a) determine c(0). interpret this value.
c(0)=80
now interpret the value of c(0). choose the correct interpretation below.
a. the value of c(0) represents the number of minutes included in the base plan.
b. the value of c(0) represents the cost per cell phone minute.
c. the value of c(0) represents the number of minutes that can be used for no charge.
d. the value of c(0) represents the monthly fee. it is the cost per month if no minutes are used.
(b) determine c(1000). interpret this value.
c(1000)=□

Explanation:

Step1: Find the slope of the line

We use two points \((m_1,C_1)=(4000,500)\) and \((m_2,C_2)=(14100,1914)\)
The slope formula is \(k=\frac{C_2 - C_1}{m_2 - m_1}\)
\(k=\frac{1914 - 500}{14100 - 4000}=\frac{1414}{10100}=0.14\)

Step2: Use the point - slope form \(C - C_1=k(m - m_1)\)

Using the point \((0,80)\) (since \(C(0) = 80\)) and \(k = 0.14\), the function is \(C(m)=0.14m+80\)

Step3: Calculate \(C(1000)\)

Substitute \(m = 1000\) into \(C(m)=0.14m + 80\)
\(C(1000)=0.14\times1000+80\)
\(C(1000)=140 + 80\)

Answer:

\(220\)