(a) Devise a function g(t) (based on the time t that Hugh reads on his watch) which gives the real time. (b) Hugh drives to Illinois from New Jersey....

(a) Devise a function g(t) (based on the time t that Hugh reads on his watch) which gives the real time. (b) Hugh drives to Illinois from New Jersey. A function which gives a good approximation of his position is f (t) = 70t. How fast did he drive? (c) Give a function which records the position of the car based on the time that Hugh reads on his watch. (d) In the time that it took to drive 70 miles, how much time elapsed on his watch? (e) What was the velocity of the car according to readings Hugh took from his watch? 6. Repeat the previous problem, but with a few changes. (a) The position of the car is now given by the function f (t) = t2 + 36t. How fast is Hugh going at time t? (b) Hughs watch is now even more severely damaged, so the real time is given by g(t) = t2 + 1/t. What function gives the position of the car based on the time on his watch? (c) What is the rate of change between the real time and the time on his watch at time t? (d) When his watch tells him that it