Student provides the correct exponential function for Ben's scenario. 2 Student provides the correct exponential function for Carter's scenario. 2
Graph is complete and accurate, and all three student graphs are shown and labeled correctly. 6
All three predictions are correct for Day 3 and Day 10. 4
Student explains correctly which post travels fastest and provides justification. 2
Student explains correctly how the new graph compares with the original. 2
Student provides complete discussion on which option he or she prefers and justifies his or her answer mathematically.

options a,b,c are the right answer.

step-by-step explanation:

a linear parent function is always represented as y = x

if we write this function in the form of y=mx+c

⇒

or  

now if we plot a graph we will find these characteristics:

1) y intercept of the graph is zero so its a straight line passing through origin.

2) as we can see in both the forms of function written, values of x and y may be either positive or negative for the positive slope means points on the graph are either in first quadrant or in third one.

3) it's slope is one.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

c

step-by-step explanation:

32

step-by-step explanation: