Linear Functions?

Question

explain, is this best described by a linear function or a non-linear function. Explain your reasoning.

a. The time it takes you to get to work as a function the speed at which you drive

b. The probability of getting into a car accident as a function of the speed at which you drive

c. A person's height as a function of the person's age (from age 0 to 100)

Answer 1

a) this is an inverse function; the faster you travel the shorter is the time it takes you to get to work

b) I would argue there is certainly a direct relationship between the two (the faster you go the more likely you are to collide), but suspect that the relationship is more complicated than linear. But, to a first approximation, the faster you go the more cars you can overtake and collide with, so this is arguably linear.

c) Definitely not linear; from 0 to teens you get taller as you get older, but from teens to middle aged you are pretty much constant in height, and from some age (60? on) you actually shrink a little with height as your spine compresses, so this is definitely not a linear function in the age range of 0 to 100

Answer 2

a. linear. relation between time and velocity, huh? check your physics book =)
b. linear too. there is a research about this.
c. it's a curve. humans arent plant. they stop growing at certain age.

Answer 3

a. Non-linear, because the time it takes to get to work is inversely proportional to speed, not directly proportional.

b. It might be linear, but we don't really have enough information to say.

c. Non-linear, because growth is much more rapid between the ages of 0 and 20, with spurts and lulls, and with little or no growth after that point.

Answer 4

a) non-linear; you have to stop and start.
b) non-linear; as your speed increases, the probability increases drastically
c) non-linear; you start small, grow to a max, then start shrinking