AlgebraEasy–MediumInterpreting the slope of a cost function
Algebra practice question
The cost, in dollars, of renting a rowing boat for h hours is given by C(h) = 6.5h + 12. What is the best interpretation of the number 6.5 in this context?
- A. The rental cost increases by $6.50 for each additional hour.Correct
- B. The boat costs $6.50 to rent for any number of hours.
- C. The boat must be rented for at least 6.5 hours.
- D. The fixed charge for renting the boat is $6.50.
Answer: A. The rental cost increases by $6.50 for each additional hour.
In C(h) = 6.5h + 12, the coefficient 6.5 is the slope: the cost per hour. The 12 is the fixed charge.
Why the other answers are wrong
- B. The boat costs $6.50 to rent for any number of hours.
- The cost depends on h; 6.5 is per hour.
- C. The boat must be rented for at least 6.5 hours.
- 6.5 multiplies h; it is not a minimum time.
- D. The fixed charge for renting the boat is $6.50.
- The fixed charge is 12, the constant term.
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