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Chapter 2: Problem 10

A shaved ice stand located near a beach records its hourly revenue as well as the temperature outside, as shown on the graph above. Approximately how much more revenue would be expected during a 3-hour shift with a temperature of \(100^{\circ}\) than at a shift of the same duration with a temperature of \(90^{\circ}\) ? A. $$\$ 150$$ B. $$\$ 500$$ C. $$\$ 750$$ D. $$\$ 1,500$$

Short Answer

Expert verified
Based on the given steps, first, determine the relationship between the temperature and hourly revenue from the graph. Subsequently, calculate the revenue at 100°F and 90°F using the obtained relationship, then multiply the hourly revenue by 3 for each case. Finally, find the difference in revenue between the 3-hour shifts at these two temperatures and select the correct answer choice.

Step by step solution

01

Determine the relationship between temperature and hourly revenue

Since the relationship is given in a graph, estimate how the hourly revenue changes with temperature. If it's a linear relationship, it's better to find the slope.
02

Calculate the revenue at 100°F and 90°F

Let's assume we have found out the relationship between temperature and the hourly revenue. Now we can calculate the revenue at both temperatures. Consider the hourly revenue function as R(T), where T stands for temperature. Find R(100) and R(90) by substituting the values of T.
03

Calculate the revenue for each 3-hour shift

To find the revenue during a 3-hour shift, multiply the hourly revenue by 3. Calculate the revenue for both temperatures: 3 * R(100) and 3 * R(90).
04

Calculate the difference in revenue

Now, subtract the revenue of the 3-hour shift at 90°F from the revenue at 100°F: (3 * R(100)) - (3 * R(90)).
05

Choose the correct answer

Check the available options and select the answer that matches the result calculated in step 4.

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