Question

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

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

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.

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.

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).

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)).

Choose the correct answer

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