Question

pablos family is on vacation at stony shore lake, and they want to rent a kayak. the kayak rental company provides the table below so customers know how much it costs to rent a kayak for 2, 3, 6, or 7 days. the cost of a rental includes a base charge for the kayak plus a daily fee. rental time in days (t) | total cost (c) 2 | $120 3 | $165 6 | $300 7 | $345 complete the sentence. pablos family will pay a base charge of $ and a fee of $ per day to rent a kayak. submit work it out not feeling ready yet? these can help: write a linear equation from a graph (0) write a linear equation from two points write a linear function from a table (100) write a linear equation from a slope and a point interpret the slope and y - intercept of a linear function write linear functions: word problems

Explanation:

Step1: Find the daily fee (slope)

The daily fee is the slope of the linear relationship between rental time (\(t\)) and total cost (\(C\)). Using two points, e.g., \((2, 120)\) and \((3, 165)\), the slope \(m\) is calculated as \(\frac{165 - 120}{3 - 2}=\frac{45}{1} = 45\). So the daily fee is \$45.

Step2: Find the base charge (y-intercept)

Using the linear equation \(C = mt + b\) (where \(b\) is the base charge), substitute \(t = 2\), \(C = 120\), and \(m = 45\): \(120 = 45(2)+b\). Solving for \(b\): \(120 = 90 + b\), so \(b = 120 - 90 = 30\). The base charge is \$30.

Answer:

Base charge: \$30, Daily fee: \$45