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Math  /  Data & Statistics

Question1. Find the rate of change (cost per hour) for renting the equipment from a local hardware store if the rate of change is constant. \begin{tabular}{|l|l|l|} \hline hours & 11 & 14 \\ \hline cost & $91\$ 91 & $109\$ 109 \\ \hline \end{tabular} a) 18\frac{1}{8} b) 8 c) 10 d) 16\frac{1}{6} e) 6

Studdy Solution

STEP 1

1. The cost of renting the equipment changes at a constant rate with respect to time.
2. The rate of change is defined as the change in cost divided by the change in hours.

STEP 2

1. Identify the change in cost.
2. Identify the change in hours.
3. Calculate the rate of change (cost per hour).

STEP 3

Identify the change in cost:
The cost at 14 hours is \$109, and the cost at 11 hours is \$91. Calculate the change in cost:
ΔCost=109−91=18 \Delta \text{Cost} = 109 - 91 = 18

STEP 4

Identify the change in hours:
The hours change from 11 to 14. Calculate the change in hours:
ΔHours=14−11=3 \Delta \text{Hours} = 14 - 11 = 3

STEP 5

Calculate the rate of change (cost per hour):
The rate of change is the change in cost divided by the change in hours:
Rate of Change=ΔCostΔHours=183=6 \text{Rate of Change} = \frac{\Delta \text{Cost}}{\Delta \text{Hours}} = \frac{18}{3} = 6
The rate of change (cost per hour) is:
6 \boxed{6}

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