The approximate number of accidents in one month, N, involving drivers between 16 and 30 years of age inclusive can be approximated by the equation or function N(a)=2a^2-80a+5000 where a= age of driver.
Calculate n(20) and explain what this answer means.
What is the domain of this function?
Can this function be used to calculate the approximate number of accidents for people my grandfathers age (65 years)? why or why not?
a is the age of the drivers. N is the number of accidents for drivers aged a. For example, there are 4200 accidents involving 20-year-old drivers. That's what N(20) means. N(a) means that the number of accidents is a function of the age of the driver. Ask youself this question: "How many accidents are there?" The answer must be: "That depends on the age of the driver." because withouth knowing the age, you can't determine how many accidents. This is basically what "N is a function of a" means. You could also use f(x) in the same way to say "f is a function of x" (you need to know what x you are talking about to figure out what f is - both can vary).
Domain is defined as: all possible numbers that can be input to give you a valid output. In the case of this equation for the number of accidents, the equation is - by definition - valid only for ages 16 to 30. For example, could you calculate the number of accidents involving drivers aged -3 years old? After all, you could plug -3 into the equation: .
Does this mean that there are 5258 accidents involving drivers aged -3? Of course not. The result is absurd. A driver must be at least positively aged!! And you couldn't input an age of 65 into the equation either. Again, you are told this in the problem statement: the equation is only valid for ages between 16 and 30. The only valid input for this equation are the numbers between 16 and 30. Thus, the domain of the function N is 16<a<30 (could be equal to as well if you somehow interpret 'between' as being inclusive).