Function Word Problem: Find linear fcn for calories burned

[Carl55]

I recently had a function problem that I got wrong, and honestly have no idea how to do. I have done okay up to this point on the functions, but the word problem is really throwing me off. Here is the problem:

The number of calories burned for 1 hour on a treadmill going at a constant speed is a function of the incline of the treadmill. At 4 miles per hour an average person on a 5° incline will burn 525 calories. At 4 mph on a 15° incline the average person will burn 880 calories. Let C be the calories burned and d be the degrees of incline of the treadmill. Determine a linear function, C(d), that fits the data. Be sure to begin your response with C(d)=, but do not include any spaces in your answer.

The answer is:

C(d)=35.5d+347.5

I have tried everything I can think of and cannot get either of those numbers. Any help on the steps taken or how to set up a problem like this would be greatly appreciated.

Thank you in advance for any help,
-Carl

 

[Loren]

Re: Function Word Problem

You have two points on a graph. They are P[sub:3z8t5j1e]1[/sub:3z8t5j1e](5,255) and P[sub:3z8t5j1e]2[/sub:3z8t5j1e](15,880). Derive the formula for the straight line that passes through these two points. You can either determine the slope of the line then use the slope-intercept form or simply use an equation you don't see too often, namely...
\(\displaystyle y-y_1 = \frac{y_2-y_1}{x_2-x_1}(x-x_1)\).
Plug in your values and simplify.

 

[Denis]

Re: Function Word Problem

You can also simply reason it out:

880 - 525 = 355 for 10 degrees (5 to 15) = 35.5 per degree

525 - (35.5 * 5) = 347.5

 

[Carl55]

Thank you both so much for the help. Denis, you especially made it easy to understand for me.

I appreciate you both taking your time to help me understand that problem.
-Carl