Question

Suppose the distributor charges the artist a $50.00 cost for distribution, and the streaming services pays $4.00 per one thousand streams.

Model the profit for the total number of streams by answering the questions below:
Use the cost for distribution to build your y-intercept. What is the y-intercept?
Hint: the y-intercept is a point on the y axis, so your answer should be an ordered pair. Hint: you have to keep in mind that any time you pay for something, you are SPENDING money, if your y-intercept is incorrect, all your numbers will be off
Use the payment per thousand streams to build your slope. What is the slope? Use the slope-intercept format (y = mx + b) to give the equation of the line.
What is the equation of this line?
Graph the line by adjusting the sliders below. Show your line by attaching an image below.
After how many streams will you pay for the distributor charges? (hint: this is where the line crosses the x-axis, round to the nearest thousand) How many streams would it take to profit $300,000?
Challenge Question: In 2019, Old Town Road became one of the most streamed songs of all time passing the previous record holders, Despacito and One Sweet Day. The second week the song was #1, it set an all time streaming record. It was streamed 143 million times (143,000,000) in the US, nearly 30 million higher than the previous record holder Drake, In My Feelings. Calculate the profit earned using these numbers. (Hint: use the slope intercept format to build this equation).

Answer 1

a) The value of the y-intercept is (0, -50).

b) $4 per thousand streams is the slope.

b) The straight line equation that yields profits is y = 4x - 50.

d) This solution has the graph of this function connected.

e) Following 12,500 streams, one would be eligible to pay the distributor fees.

f) It would take 75,012,500 streams to earn $300,000. g) Old Town Road would earn $571,950 if it were streamed 143,000,000 times.

Let y represent the earnings (in dollars).

There are x (in thousands) streams in the system.

When x = 0, the distribution cost is $50. In other words, since one is spending this money, when x = 0 and y = -50, the revenue for a thousand streams is $4$.

The straight line's equation is therefore y = mx + c, where m is the revenue per thousand streams and y = profits.

x is the quantity of streams (in thousand).

Cost at zero streams = c = -50

y = 4x - 50.

a) The value of the y-intercept is (0, -50).

b) $4 per thousand streams is the slope.

b) The straight line equation that yields profits is y = 4x - 50.

d) This solution has the graph of this function connected.

e) This is the x-intercept; at the point where the profit is zero, one can pay the distributor. y = 4x - 50 when y = 0. 0 = 4x - 50

50 = 4x

x = (50/4) = 12.5

After 12,500 streams, one would therefore be able to pay the distributor.

f) With y = $300,000 and x =?

y = 4x - 50

300,000 = 4 times - 50

x = (300,050/4) = 75,012; 4x = 300,050.75,012,500 streams x 5,000 streams.

g) If Old Town Road were to be streamed 143,000,000 times,

143,000,000 streams divided by 143,000 streams

In order to get the number of streams (x = 143,000), we need the earnings (y) = 4x - 50.

Answer 2

a) y-intercept is given as (0, -50)

b) Slope = $4 per thousand streams

c) Equation of the straight line that gives the profits is

y = 4x - 50

d) Graph of this function is attached to this solution

e) One would be able to pay the distributor charges after 12,500 streams.

f) One would require 75,012,500 streams to make $300,000

g) If Old Town Road was streamed 143,000,000 times, then it made $571,950.

Explanation:

Let the profits be y (In dollars)

The number of streams in be x (in thousands)

The cost of distribution, when x = 0, is $50. That is, when x = 0, y = -50 (since one is spending this money)

And the revenue for a thousand streams is 4$.

So, the equation of the straight line is given as y = mx + c

y = profits,

m = revenue per thousand streams

x = number of streams (in thousand)

c = cost incurred at 0 streams = -50

y = 4x - 50

a) y-intercept is given as (0, -50)

b) Slope = $4 per thousand streams

c) Equation of the straight line that gives the profits is

y = 4x - 50

d) Graph of this function is attached to this solution.

e) After how many streams will you pay for the distributor charges?

This is the x-intercept; one would be able to pay the distributor at the point where the profit is $0.

y = 4x - 50

when y = 0.

0 = 4x - 50

4x = 50

x = (50/4) = 12.5 ( in thousands)

Hence, one would be able to pay the distributor after 12,500 streams.

f) How many streams would it take to profit $300,000?

y = $300,000, x = ?

y = 4x - 50

300,000 = 4x - 50

4x = 300,050

x = (300,050/4) = 75,012.5 thousand streams = 75,012,500 streams.

g) How much did Old town road make if it was streamed 143,000,000 times.

143,000,000 streams = 143,000 thousand streams

So, we require the profits, y, for number of streams, x = 143,000

y = 4x - 50

y = (4×143000) - 50 = $571,950

Hope this Helps!!!