Question

At a speed of 45 yards per minute, a 120 pound swimmer burns 420 calories per hour and a 172 pound swimmer burns 600 calories per hour. write an equation that models the number of calories burned per hour as a function of the swimmer's weight.

Answer 1

c = w*45/13 + 60/13 I will be assuming that the equation will be linear since there are only 2 data points available. The form of the equation will be c = aw + b where c = calories burned a = some constant w = weight b = some other constant. If you look at the equation, you'll notice that it looks like the equation for a line i slope intercept form. So first, let's calculate the slope of the desired equation. a = (600-420)/(172-120) = 180/52 = 45/13 = 3.461538462 Now we have the equation c = w*45/13 + b Substitute the values for a known point, giving 420 = 120*45/13 + b Now solve for b 420 = 120*45/13 + b 420 = 5400/13 + b 420 - 5400/13 = b 5460/13 - 5400/13 = b 60/13 = b So now the equation is c = w*45/13 + 60/13