D(t) = (4t)/ (0.01t^2 +5.1)

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• Apr 22nd 2011, 10:21 PM
pcalhelp
D(t) = (4t)/ (0.01t^2 +5.1)
For these I'm clueless. Please help

5) Function D(t) = (4t)/(0.01t^2+5.1). Given the concentration, D, of a drug in bloodstream where D is measured in micrograms per milliliter and t is minutes from the time the drug is taken. What's the maximum concentration of the drug found in bloodstream at any time?
A) 0.01 micrograms/ milliliters
B) 4 micrograms/ milliliters
C) 5.1 micrograms/ milliliters
D) 8.856 micrograms/ milliliters
E) 22.583 micrograms/ milliliters
• Apr 22nd 2011, 10:35 PM
abhishekkgp
Quote:

Originally Posted by pcalhelp

5) Function D (t) = (4t)/ (0.01t square+5.1). Given the concentration, D, of a drug in bloodstream where D is measured in micrograms per milliliter and t is minutes from the time the drug is taken. What's the maximum concentration of the drug found in bloodstream at any time?
A) 0.01 micrograms/ milliliters
B) 4 micrograms/ milliliters
C) 5.1 micrograms/ milliliters
D) 8.856 micrograms/ milliliters
E) 22.583 micrograms/ milliliters

for this you can do the following:
D(t) = (4t)/[(0.01t)^2 +5.1] = (4)/[0.01t + (5.1/t)]
to find maximum of (4)/[0.01t + (5.1/t)] you need to find the minimum of 0.01t + (5.1/t). Use AM-GM inequality.
did this help?
• Apr 22nd 2011, 10:38 PM
pcalhelp
Quote:

Originally Posted by abhishekkgp
for this you can do the following:
D(t) = (4t)/[(0.01t)^2 +5.1] = (4)/[0.01t + (5.1/t)]
to find maximum of (4)/[0.01t + (5.1/t)] you need to find the minimum of 0.01t + (5.1/t). Use AM-GM inequality.
did this help?

How do you find the minimum? What is AM-GM?
Sorry, I;m not very good at math
• Apr 22nd 2011, 10:49 PM
abhishekkgp
Quote:

Originally Posted by pcalhelp
How do you find the minimum? What is AM-GM?
Sorry, I;m not very good at math

AM-GM inequality states that if a>0 and b>0 then a+b >= 2(sqrt(ab))

you could also check this out Inequality of arithmetic and geometric means - Wikipedia, the free encyclopedia
• Apr 23rd 2011, 10:58 AM
HallsofIvy
"AM-GM": Arithmetic Mean- Geometric Mean. The arithmetic mean of two numbers is (a+ b)/2. The geometric mean of two numbers is \sqrt{ab}. The "Arithmetic Mean-Geometric Mean inequality" says that the arithmetic mean is always less than equal to the geometric mean.

(More geherally, the arithmetic mean of n numbers, a_1, a_2, \cdot\cdot\cdot, a_n is \frac{a_1+ a_2+ \cdot\cdot\cdot+ a_n}{n} and the geometric mean is \sqrt[n]{a_1a_2\cdot\cdot\cdot a_n}. There is also the "harmonic mean". The harmonic mean of 2 numbers is \frac{2}{\frac{1}{a}+ \frac{1}{b}}. The harmonic mean of n numbers is \frac{n}{\frac{1}{a_1}+ \frac{1}{a_2}+ \cdot\cdot\cdot+ \fra{1}{a_n}}
• Apr 23rd 2011, 10:07 PM
abhishekkgp
Quote:

Originally Posted by HallsofIvy
The "Arithmetic Mean-Geometric Mean inequality" says that the arithmetic mean is always less than equal to the geometric mean.

hey halls!
there's a typo error in there! :)
• Apr 24th 2011, 07:32 AM
HallsofIvy
Quote:

Originally Posted by abhishekkgp
hey halls!
there's a typo error in there! :)

What, only one???
• Apr 24th 2011, 07:08 PM
abhishekkgp
Quote:

Originally Posted by HallsofIvy
What, only one???

i can see only one. which is(are) the other one(ones)??