Here we have an application of Linear functions involving a candy company and the second sentence here the number
of candy canes produce depends on the amount of time the machine has been
operating is very important so I’m gonna write here C depends on T. That’s another way in mathematics of saying that C is a function of T
let’s write down what each of these variables represents.C is going to be the number
of candy canes produced and T is going to be our time, in minutes and very important that you say if it’s
in minutes, or seconds, or hours, or whatever. So what we know is some information the
machine produces 160 canes in 5 minutes. So everyone of ordered pairs
is gonna look like T comma C. So this ordered pair would be 5
160. In 20 minutes the machine can produce
640. So 2640 would be another ordered pair were asked to write
a linear equation the first thing we need to write a linear equation is the
slope. So the slope I can find by using these two ordered pairs so 640 minus 160 divided by 20 minus 5 equals 400 eighty over 15 which is 32. So my slope m is 32. Well the next thing I need is my
vertical intercept. I can interpret that from the information given in this problem let me write intercept here. If I’m have produced 0 time in other words have 0 time has
passed I can make 0 candy cane so 0,0 will be my vertical intercept that means
I can write an Equation C equals 32 T plus 0. So lets write that in
function notation. C of T equals 32t their is my own many require usual and
that models this situation. Determine the vertical intercept well we
already did that that is 0.0 the vertical intercept means that at time equal 0 no canes have been produced. If I want the horizontal intercept well that’s the same ordered pair we’re just looking at when is the output 0 when the input is zero so here we would
say when no canes are made no time has passed. So it’s kinda
the reversed situation and in part D then how many candy canes with the
machine produce in one minute well that’s C of one time is one minutes so 32 times one equals 32 and I have that the machine will
produce thirty two canes in one minute how many will the machine
produce in an hour well an hour that’s sixty minutes
don’t just put one because then that would not be the right
units so 32 times sixty equals 1920 and what we can say then is that the
machine produces 1,920 canes in one hour.