Production over time: Let’s say every hour(x) I get five dollars (y). That should look something like. (24x X 5y) = 120

[Joisarri]

Hi, Im confused over what I know is supposed to be a really simple equation, but I’ve simply forgotten how to go about equating it. So here goes my question.

Let’s say every hour(x) I get five dollars (y). That should look something like. (24x X 5y) = 120
However, 12 hours in I get a raise of two dollars
So halfway in it starts to look like (12x X 7y) = 84

How do I merge these two?

 

[Otis]

every hour(x) I get five dollars (y). That should look something like. (24x X 5y) = 120

Hi Joisarri. In algebra, we always define our symbols first. That way, we can see if our expressions make sense.

Your equation above implies that you may be thinking x represents 1hr and y represents $1. That won't work because we cannot multiply 24*1hr by 5*$1. (The result would be 120hour-dollars.)

Within the first 12 hours, I'm thinking something like this:

Let x = elasped time (in hours)
Let y = total money received at time x (in dollars)

y = 5x

So, are you trying to come up with a formula where you substitute any number of elapsed hours (for x), to get the value of y at that point?

If so, then are you also incorporating the formula within software that you're developing?

I ask because the growth rate of money received changes after 12 hours (from $5/hr to $7/hr), and that situation requires what's known as a piecewise construction – one formula used when x goes from 0 through 12 and a second formula when x is greater than 12.

Please provide more details about why you desire the formula (i.e., what you plan to do with it). Also, if this is schoolwork, then please provide the complete text of the project statement. We can go from there. Cheers!

PS: We're using x as a variable, so let's not use X as a multiplication sign. Use an asterisk, instead.
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[Steven G]

Think of it like this. You work two jobs. One for 12 hours and the other job for 12 hours.
Suppose the 1st job pays you $5/hr, while the 2nd job pays for $7/hr. I bet you can finish from here. Just understand that how much you make from one job does not affect how much you make from the other job.

Alternatively you can compute 24*$5 = $120 and then add on 12*$2 =$24 for the amount you earned from the $2/hr raise. The total is $144.

Another way: Since you are working the same number of hours for each pay rate you can just think that for the 24 hours you will be earning the average of $5 and $7 which is $6. Now 24*$6 = $144

 

[Joisarri]

Hi Joisarri. In algebra, we always define our symbols first. That way, we can see if our expressions make sense.

Your equation above implies that you may be thinking x represents 1hr and y represents $1. That won't work because we cannot multiply 24*1hr by 5*$1. (The result would be 120hour-dollars.)

Within the first 12 hours, I'm thinking something like this:

Let x = elasped time (in hours)
Let y = total money received at time x (in dollars)

y = 5x

So, are you trying to come up with a formula where you substitute any number of elapsed hours (for x), to get the value of y at that point?

If so, then are you also incorporating the formula within software that you're developing?

I ask because the growth rate of money received changes after 12 hours (from $5/hr to $7/hr), and that situation requires what's known as a piecewise construction – one formula used when x goes from 0 through 12 and a second formula when x is greater than 12.

Please provide more details about why you desire the formula (i.e., what you plan to do with it). Also, if this is schoolwork, then please provide the complete text of the project statement. We can go from there. Cheers!

PS: We're using x as a variable, so let's not use X as a multiplication sign. Use an asterisk, instead.
[imath]\;[/imath]

Ahh thank you for volunteering to help me, and for correcting me, haha.

This isn’t for any homework, it’s entirely for self entertainment purposes. (a numbers game.)

I was attempting to use Desmos in order to visualize long term growth, but as you’ve noticed, I don’t fully understand the equation I’m trying to input.

 

[Otis]

I was attempting to use Desmos

Hi. I found the syntax for piecewise plots (in the user's guide). Seemingly, Desmos allows for only two pieces per plot command.

y = {first x-interval:first y-expression,second y-expression}

For your project, each plot command graphs one day as two 12-hour intervals. For Day1, the first x-interval is 0<x<12, and the expression for y is 5x. In the second 12-hour interval (which we don't enter), y is 7x–24. To prevent the second piece from graphing beyond its interval, we insert a domain statement (for the whole day) after the second y-expression:

{starting x-value<x<ending x-value}.

So, that domain statement would be 0<x<24 for the Day1 plot. Plot commands for subsequent days come from increasing each parameter value in the previous plot by 24 (shown in bold below).

Here are plot commands covering the first three days. (If you copy-and-paste them, you might need to manually insert the curly braces.)

y = {0<x<12:5x,7x-24{0<x<24}}

y = {24<x<36:5x+24,7x-48}{24<x<48}}

y = {48<x<60:5x+48,7x-72}{48<x<72}}

After adjusting display settings, the Desmos graph looks like this. For longer-term growth, I might use a spreadsheet to generate lists of data.


[imath]\;[/imath]

 

[Joisarri]

Hi. I found the syntax for piecewise plots (in the user's guide). Seemingly, Desmos allows for only two pieces per plot command.

y = {first x-interval:first y-expression,second y-expression}

For your project, each plot command graphs one day as two 12-hour intervals. For Day1, the first x-interval is 0<x<12, and the expression for y is 5x. In the second 12-hour interval (which we don't enter), y is 7x–24. To prevent the second piece from graphing beyond its interval, we insert a domain statement (for the whole day) after the second y-expression:

{starting x-value<x<ending x-value}.

So, that domain statement would be 0<x<24 for the Day1 plot. Plot commands for subsequent days come from increasing each parameter value in the previous plot by 24 (shown in bold below).

Here are plot commands covering the first three days. (If you copy-and-paste them, you might need to manually insert the curly braces.)

y = {0<x<12:5x,7x-24{0<x<24}}

y = {24<x<36:5x+24,7x-48}{24<x<48}}

y = {48<x<60:5x+48,7x-72}{48<x<72}}

After adjusting display settings, the Desmos graph looks like this. For longer-term growth, I might use a spreadsheet to generate lists of data.

View attachment 35508
[imath]\;[/imath]

Ok ok, while slightly less automated than I expected, this does do for what I needed help for. Thank you!

 

[Otis]

slightly less automated than I expected

Hi. I haven't used Desmos enough to be sure, but (for a graphing calculator) it doesn't seem to have much automation.

If you share some detail about your numbers game, then we might have other suggestions. Otherwise, I'm glad you that you get something useful out of the Desmos graph. Cheers
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