5 part problem w/3 equations y = 0.75*, y=0.25*, y=-0.5*+1

[cornhusker1231]

Can anyone help me with this problem? My mom who has a masters in math doesn't understand it. Do you?

Consider these three equations:

y = 0.75*
y = 0.25*
y = -0.5* + 1

a. Sketch the graphs of all three equations on one set of axes.

b. What points, if any, do the three graphs have in common?

c. In which graph does the y value decrease at the greatest rate as the x value increases?

d. How can you use your graphs to determine which of the equations is not an example of exponential decay?

e. How can you use the equations to determine which one is not an example of exponential decay?

 

[jwpaine]

Do you mean...

y=0.75x
y=0.25x
y=-0.5x +1

?

If so, graph the line which is in standard form y=mx+b
your y intercept = 0, so you know each line passes through the point of origin. (0,0)

What points do the three graphs have in common? Think about what I said, above.

for c, if you plug in a increasing values for y= -0.5(x) +1 then y will be getting smaller, because of the negative sign of ax (a negative times a positive = a negative)

 

[sk19math]

Actually... now that I am looking at it.... Should your equations be like:

y= 0.75^x???? (As in, 0.75 to the power of x)...

Because that changes things... could you clarify that part please?




Assuming that your equations were indeed missing the X variable, the last comment isn't entirely accurate... not all 3 of the lines go through (0,0).

By comparing to y=mx+b, you can see that the first 2 indeed have no stated b-value (so b=0), so those pass through the origin... but the third one has a b=1, so it intercepts the y-axis at (0,1).

To answer b), you can graph the 3 lines to see if they all intersect at a common point... but I don't think they will. Given that they are straight lines, and they do not curve back onto themselves at all, 2 lines will only ever intersect at a single point. Try that with any 2 straight lines, or use 2 pencils, or whatever, to convince yourself of that.

So we just established that the first 2 lines pass through the origin, but the third doesn't. Therefore, lines 1 and 2 meet at the origin, but lines 1 and 3, and 2 and 3, must meet somewhere else... and so all 3 points do not meet at a single common point.

For part c), you just need to look at the slopes of the lines... which one has the y-value decreasing the most as x increases... (Hint... which one has the y-value decreasing... period).

Parts d and e lead me to think you are talking about exponents......