SOLUTION: This is another one that I'm stuck on. This is probably so basic but it's been a VERY long time. Please help! Thanks 4. For each of the relationships below, explain whether y

Click here to see ALL problems on Functions

Question 165543: This is another one that I'm stuck on. This is probably so basic but it's been a VERY long time. Please help! Thanks

4. For each of the relationships below, explain whether you think it is best described by a linear function or a non-linear function. Explain your reasoning thoroughly
a. A person's height as a function of the person's age (from age 0 to 100)
b. The probability of getting into a car accident as a function of the speed at which you drive
c. The time it takes you to get to work as a function the speed at which you drive
Found 2 solutions by gonzo, josmiceli:
Answer by gonzo(654) (Show Source):
You can put this solution on YOUR website!
a. A person's height as a function of the person's age (from age 0 to 100)
-----
i would say non-linear.
there is a large growth spurt in the early years and then it tapers off to about nothing for a long period of time.
-----
b. The probability of getting into a car accident as a function of the speed at which you drive.
-----
again i would say non-linear.
there does not appear to be a straight line correlation.
some studies show it as exponential.
there are also too many variables involved to isolate speed as a directly causative factor unless it's far in excess of what's considered reasonable.
if you go to extremes, then it's clear that there's a positive correlation and i would estimate exponential increases in the probability of having an accident the faster you go with small increases early on but much bigger as you get up there.
example would be going down a city street.
at 25 p(a) is very small.
at 30 still small.
at 35 still small.
at 40 still small but getting bigger.
at 50 bigger.
at 60 much bigger.
it goes up astronomically from there.
-----
c. The time it takes you to get to work as a function the speed at which you drive
-----
this is also non-linear.
it's more of a ratio, i.e. time to get there = distance / speed.
-----
you can use straight lines to provide regression analysis, but a curve fitting program that finds an equation that fits the data would be more suitable.
an online version of one is at this internet address.
-----
http://people.hofstra.edu/Stefan_Waner/RealWorld/newgraph/regressionframes.html
-----
if you plot some points you can see which of the curves fits best. none of them are perfect, except for the last one that you asked (speed versus time to get to work, the equation of y = ax^b seemed to work best. in my test data the equation worked out to be y = 100x^-1 which translated to y = 100/x. where y was the time to get to work, 100 was the miles to get to work (a), and x was the speed.

Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
These are "thinking" problems. You have to have a
clear picture of linear vs non-linear
price/item x # of items is linear (unless there's a sale)
price/pound x pounds purchased usually is non-linear if
the pounds go way up
(a) is non-linear you don't grow as much from
80 to 100 as you do from 0 to 20
(b) non-linear because going from 30 mph to 70 mph
is not as bad as 70 mph to 110 mph
(c) I think it's non-linear because the faster you drive
the likelihood of an accident or getting stopped goes up