Calculus question

Question

The number of fatalities due to car crashes, based on the number of miles driven, begins to climb after the driver is past age 65. Aside from declining ability as one ages, the older driver is more fragile. The number of fatalities per 100 million vehicle miles driven is approximately

N(x) = 0.0336x³ − 0.118x² + 0.215x + 0.7     (0 ≤ x ≤ 7)

where x denotes the age group of drivers, with x = 0 corresponding to those aged 50–54, x = 1 corresponding to those aged 55–59, x = 2

 corresponding to those aged 60–64, …, and x = 7

 corresponding to those aged 85–89.† What is the fatality rate per 100 million vehicle miles driven for an average driver in the 50–54 age group? In the 55–59 age group?

50–54 fatalities/100 million miles55–59 fatalities/100 million miles

   

Answer 1

I don't see this as necessarily a calculus question. You've given a cubic function for which N(x) is the "number of fatalities per 100 million". The function value N(x) seems to be the "rate" you're looking for, at least the way you described the problem. Plugging in the numbers, N(1)=0.8306 for 50-54 year-olds, and N(2)=0.9268. You haven't given the units N(x) is supposed to be in. If it's 100's of millions, that means N(1) is 83 million fatalities, absurdly high. Millions means N(1) is 830,000 fatalities, still pretty high. It might make sense as hundreds of thousands or tens of thousands; I don't know. There are applications of derivatives and integrals for this function, but they don't seem to be what you are describing.