Question

ryan works for a delivery service. the function $f(n)$ is used to calculate his daily pay, in dollars, on a day when he makes $n$ deliveries. $f(n) = 7n + 96$ use the function to complete the table shown. \

$$\begin{tabular}{|c|c|} \\hline number of deliveries & daily pay (dollars) \\\\ \\hline 0 & \\fbox{i} \\\\ \\hline 5 & \\fbox{} \\\\ \\hline \\fbox{} & 145 \\\\ \\hline \\end{tabular}$$

Explanation:

Step1: Calculate pay for \( n = 0 \)

Substitute \( n = 0 \) into \( f(n)=7n + 96 \).
\( f(0)=7\times0 + 96 = 96 \)

Step2: Calculate pay for \( n = 5 \)

Substitute \( n = 5 \) into \( f(n)=7n + 96 \).
\( f(5)=7\times5 + 96 = 35 + 96 = 131 \)

Step3: Find \( n \) for pay \( 145 \)

Set \( f(n)=145 \), so \( 7n + 96 = 145 \).
Subtract \( 96 \) from both sides: \( 7n = 145 - 96 = 49 \).
Divide by \( 7 \): \( n=\frac{49}{7}=7 \).

Answer:

For \( n = 0 \), daily pay is \( 96 \); for \( n = 5 \), daily pay is \( 131 \); for daily pay \( 145 \), number of deliveries is \( 7 \). So the completed table cells (from top to bottom, left to right for the empty ones) are \( 96 \), \( 131 \), \( 7 \).