word problem with radical

[glennda5]

5) For the following function, C computes a value, where if you add millions of dollars to the value, the result is the cost of implementing a city recycling project when x , as a percent (not its decimal equivalent), citizens participate.

C(x)=1.5x/100-x

a) Using this model, determine the cost if 60% of the citizens participate?

C (.60)=1.5x/100-.60, would this be an accurate equation, I dont seem to be coming up with a valuable answer and how do determine the cost without using decimel form for 60%?

b) Using this model, find the percentage of participation that can be expected if $5 million is spent on this recycling project? Set up an equation and solve algebraically. Round to the nearest whole percent.

I need help making the equation to solve 5(x) 1.5x/100-x i don't know how to make the equation to solve.

 

[mmm4444bot]

… C computes a value, where, if you add millions of dollars to the value, the result is the cost of implementing a city recycling project when x, as a percent (not its decimal equivalent), citizens participate …

Clearly, C is a dollar amount. But how does one know how many "millions of dollars" to add to C ?

Did your instructor write the above, or are you trying to paraphrase the actual instructions that you were given?

It make more sense, to me, to say something like the following.

C(x) = 1.5x/(100 - x) The parentheses around the denominator are VERY important.

(They show everybody the correct order of operation.)

Function C gives the cost (in millions of dollars) of implementing a city recyling project when x% of citizens participate.

For example, if 25% of citizens participate in the recycling plan, then C(25) represents the cost of implementing that plan.

C(25) = (1.5)(25)/(100 - 25) = 0.5

With 25% participation, the cost of implementation is $500,000 (i.e., half of one million).

C(60) represents the implementation cost when 60% of citizens participate.

To find the participation percent when the implentation cost is $5 million, you need to solve the following equation for x.

5 = 1.5x/(100 - x)

Here's an extra note that is not a part of this exercise. Function C is a model. This particular model only works for a certain domain of percents.

What happens if the city is lucky enough that 100% of its citizens recycle? The model crashes because we end up with division by zero.

What happens if the city is lucky enough that 90-99% of its citizens recycle? If you look at a graph of C(x) over the domain [0,100), then you'll see that the implementation costs simply "explode".

C(90) = 13.5
C(95) = 28.5
C(99) = 148.5

 

[glennda5]

I posted the question exactly how the instructor gave me the problem with no parenthesis

 

[mmm4444bot]

I'm not asking whether or not your instructor wrote parentheses.

I'm asking whether or not your instructor told you to add "millions of dollars" to the value C.

With respect to the parentheses, I'm not asking anything. I'm telling you to type them.

If you do not use parentheses as needed when typing mathematical expressions, then how are we supposed to know the correct order of operations?

The following are not the same.

1.5x/100 - x

1.5x/(100 - x)

In the former, x is subtracted from the fraction 1.5x/100.

In the latter, 1.5x is divided by 100 - x.

(By the way, why do you think there is a radical in this exercise? Did your instructor tell you that, too?)

 

[glennda5]

yes the answer to your question is adds millions of dollars to the value, the result being the cost. I appreciate your help. For some reason I am stuck and can't solve this problem i am getting confused with the cost for the answer.

 

[Deleted member 4993]

5) For the following function, C computes a value, where if you add millions of dollars to the value, the result is the cost of implementing a city recycling project when x , as a percent (not its decimal equivalent), citizens participate.

C(x)=1.5x/100-x

I posted the question exactly how the instructor gave me the problem with no parenthesis

Your teacher may have given you the following:

\(\displaystyle C(x) \, = \, \frac{1.5x}{100-x}\)

In regular ASCII for mat - it must be written with parenthesis, otherwise it does not make sense.

a) Using this model, determine the cost if 60% of the citizens participate?

C (.60)=1.5x/100-.60, would this be an accurate equation, I dont seem to be coming up with a valuable answer and how do determine the cost without using decimel form for 60%?

b) Using this model, find the percentage of participation that can be expected if $5 million is spent on this recycling project? Set up an equation and solve algebraically. Round to the nearest whole percent.

I need help making the equation to solve 5(x) 1.5x/100-x i don't know how to make the equation to solve.

 

[mmm4444bot]

yes the answer to your question is adds millions of dollars to the value …

… For some reason I am stuck and can't solve this problem ….

I do not think that you need to add "millions of dollars" to anything. I think that's your instructor's way of telling you that values from the cost function are to be interpreted as millions of dollars.

EG:

If C(x) turns out to be 2, then it means 2 million dollars.
If C(x) turns out to be 3, then it means 3 million dollars.
If C(x) turns out to be 4.5, then it means 4.5 million dollars.
If C(x) turns out to be 11, then it means 11 million dollars.
et cetera …

If you're still stuck, then we won't know the reason why until you tell us. If you are not able to form specific questions about this exercise, then please post your work so that we can try to guess what you're thinking.

DO YOU UNDERSTAND ALL OF THE FOLLOWING EXPLANATION AND EXAMPLE?

C(x) = 1.5x/(100 - x)

Function C gives the cost (in millions of dollars) of implementing a city recyling project when x% of citizens participate.

For example, if 25% of citizens participate in the recycling plan, then C(25) represents the cost of implementing that plan.

C(25) = (1.5)(25)/(100 - 25) = 0.5

With 25% participation, the cost of implementation is $500,000 (i.e., half of one million).

If there is any part of this explanation and example that you do not understand, then let me know, and we'll go from there.