Question

:)

Answer 1

They seem fairly straightforward even though the questions are very long.

y = 1907x

i) plug x = 40 and calculate y

ii) Find the slope 'm' of y = 1907x

Answer 2

yes. The total number of views 40 days after the clip was posted is 76,280.

Answer 3

ehhhhh...I dunno o.o

Answer 4

@Ashleyisakitty @superhelp101 @e.mccormick @ganeshie8

Answer 5

gradient = slope, and yes, that is rise over run. For y = 1907x, that is not 1.

Answer 6

Slope-intercept form: \(y=mx+b\) where m is slope and b is the y intercept.

Lets put \(y = 1907x\) in that form. Hmm. Something seems missing. Well, nothing seems missing. So lets add nothing since it is not there:

\(y = 1907x+0\)

Does that look like \(y=mx+b\) now? So what is m?

Answer 7

Yes.

Answer 8

Yah, it was so simple you messed yourself up looking for something more complex.

Answer 9

OK, so "What does this measure in the practical situation being modeled?" Have an answer for that one now?

Answer 10

Yes, that is a good answer. If you multiply by days then it is views per day.

Answer 11

np. have fun!

Answer 12

I have to go out for a few hours in about 5 minutes. But before I go...
y = 2140x - 53500 for 25 <= x <= 365
"calculate the day when the number of views of clip B exceeds 100 000"
y > 100, 000. Therefore, 2140x - 53500 > 100,000
solve for x. double check if the x value is in the domain: 25 <= x <= 365

Answer 13

(ii) Explain, in terms of the practical situation being modeled, why this equation does not hold for values of x less than 25.
y = 2140x - 53500
Set it to zero and solve for x.
Since you cannot have "negative number of views", x has to be greater than or equal to the value you get when you solve for x in 2140x - 53500 = 0

Answer 14

iii) sketch the graph y = 2140x - 53500 in the domain 25 <= x <= 365
It is linear and so the graph will be a straight line. Just get two convenient points and join them by a ruler. Use proper x and y scales.
Plot y = 1907x.
Don't plot for x < 0 because negative days is not meaningful.

Answer 15

Find out where the two straight lines intersect and read off the x-values. Can be solved algebraically also.

Answer 16

see ya. The last part in by previous reply they want you to do it algebraically and not graphically. So solve for x in 2140x - 53500 = 1907x.

Answer 17

For Video B:
i) Correct. On day 72, the number of views will exceed 100,000
ii) Correct but need more explanation. When x = 25, the number of views 'y', given by the equation y = 2140x-53500 is zero. Therefore, if x < 25, the number of views in the equation will be negative which is meaningless. Hence the equation is good only for x >= 25.
iii) Sketch y = 2140x - 53500 but remember, the domain is 25 <= x <= 365
When x = 25, y = 0
When x = 365, y = 727,600
The graph should not exist to the left of x = 25 or to the right of x = 365

Answer 18

Just noticed, for iii) they want to limit the plot from x = 25 to x = 300
when x = 300, y = 588,500

Answer 19

iii) cont'd plot y = 1907x on the same axes from x = 25 to x = 300
when x = 25, y = 47,675
when x = 300, y = 572,100

Answer 20

iv) Yes, when x = 230, the total number of views of videos A and B will be approximately the same.

Last question:
y = 50 * 1.5^x 1 <= x <= 30
i) Calculate the total number of views 10 days after the date of posting, x = 10.
when x = 10, y = 50 * 1.5^10 = 2883 views

(ii) Write down the scale factor, and use this to find the percentage increase in the number of views each day.
Scale factor = (y value when x = 2) / (y value when x = 1) (or ratio of y at any day divided by y at previous day)
Scale factor = (50 * 1.5^2) / (50 * 1.5^1) = 1.5

Scale factor of 1.5 means the total number of views by the end of any day will be 1.5 times the total number of views by the end of the previous day.
Percentage increase in daily viewership = (1.5 - 1) / 1 * 100 = 50%

Answer 21

The x and y value of the coordinates of two points on each line gives an idea of the magnitude of the numbers along the x and y axis.

Answer 22

Since I did not draw to scale on a proper graph paper, my markings won't be evenly spaced. But if you draw it on a proper graph paper or online tool, a scale of 50 per unit along the x-axis and 50,000 per unit along the y-axis should work fine.