The concentration C of a drug in a patient’s bloodstream: use a calculator to approximate...

[wendy218]

i cant seem to figure out this problem; it seem as though they did not finish telling you more than what it suppose to ask. please help. im assuming were trying to use the quotient rule but yet i can not seem to understand how to solve this question


The concentration C of a drug in a patient’s bloodstream t hours after injection is given by C(t)=(160t5t)/(2+120) . Use a calculator to approximate the time when the concentration is highest.

Round your answer to two decimal places.


The concentration is highest after _____ hours.

 

[wendy218]

am i suppose to keep testing to see what i get that is highest?

 

[stapel]

The concentration C of a drug in a patient’s bloodstream t hours after injection is given by C(t)=(160t5t)/(2+120) .

What is the meaning of "160t5t"? As written, it is the product [imath](160t)(5t)[/imath]. Was this what you meant?

Also, why is the denominator given as "2+ 120" rather than the simplified form [imath]122[/imath]?

Use a calculator to approximate the time when the concentration is highest.

What did you see when you plugged the given function into your calculator, and looked at the graph?

 

[Dr.Peterson]

The concentration C of a drug in a patient’s bloodstream t hours after injection is given by C(t)=(160t5t)/(2+120) . Use a calculator to approximate the time when the concentration is highest.

I suppose you copied the formula incorrectly; perhaps it is something like C(t)=(160+5t)/(2+120t)? Or maybe there is supposed to be an exponent somewhere, and you failed to indicate that.

But any variation I try doesn't look like it would have a maximum.

Please show us an image, or at least an exact copy, of the problem!

Also, is it implied that they want you to use a graphing calculator? If not, then, yes, they might want you to plug in various numbers until you find an apparent maximum. (There are other ways, but they use more than algebra.)

im assuming were trying to use the quotient rule but yet i can not seem to understand how to solve this question

What "quotient rule" are you referring to? Are you in fact taking calculus, not algebra? We need to know a lot more about your context.

Try to ask your question as thoroughly as you'd like them to ask theirs!

 

[Steven G]

am i suppose to keep testing to see what i get that is highest?

No! The question clearly asked you The concentration is highest after _____ hours. They are asking you for a special time, ie they are asking you for t, NOT the highest concentration (ie Q).
To be clearer, they are asking you for the t values that yields the largest Q value.

 

[khansaheb]

C(t)=(160t5t)/(2+120)

What does that mean? especially

160t5t ?

 

[Dr.Peterson]

The concentration C of a drug in a patient’s bloodstream t hours after injection is given by C(t)=(160t5t)/(2+120) . Use a calculator to approximate the time when the concentration is highest.

Round your answer to two decimal places.

The concentration is highest after _____ hours.

Looking for similar problems, I found these problems, with the same wording but different functions:

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I initially tried copying and pasting, and it ended up like this:

For the following exercises, use the given rational function to answer the question.​

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82.​

The concentration C of a drug in a patient’s bloodstream t hours after injection is given by C(t)=2t3+t2. What happens to the concentration of the drug as t increases?​

​

83.​

The concentration C of a drug in a patient’s bloodstream t hours after injection is given by C(t)=100t2t2+75. Use a calculator to approximate the time when the concentration is highest.​

I suspect that you did something similar; perhaps you pasted, saw C(t)=160t5t2+120, and edited it to C(t)=(160t5t)/(2+120) rather than what it really is, C(t)=(160t)/(5t^2+120): [math]C(t)=\frac{160t}{5t^2+120}[/math]
Is it that, or something similar?

The context of these problems indicates that you would be studying rational functions (which may relate to what you meant by "quotient rule"), and are expected to use a graphing calculator. Use that (or Desmos) to graph y=(160x)/(5x^2+120), and you'll find that there is, indeed, a maximum on the graph, and the tool can estimate the value of t that you need.