# Math Help - Medication Problem

1. ## Medication Problem

Just been having a little problem with this one, was hoping you guys could point me in the right direction:

Evan and Chelsea are given the same medication. However, due to their different weights and metabolic rates the dosages and the rates at which the medication leaves their systems are different. The following functions describe the concentration of medicine in their blood streams,C, with respect to time, T, in hours.

$Evan:C=80(1/2)^1/2$ $Chelsea:C=40(1/2)^1/3$

The exponents are actually 1/2 and 1/3 respectively, I'm not sure how to show a fraction in the exponent here.

A.) Who had to take the higher dosage. Explain.
B.) Whose system got rid of the medication at a faster rate? Explain.

2. Originally Posted by Vesicant
Just been having a little problem with this one, was hoping you guys could point me in the right direction:

Evan and Chelsea are given the same medication. However, due to their different weights and metabolic rates the dosages and the rates at which the medication leaves their systems are different. The following functions describe the concentration of medicine in their blood streams,C, with respect to time, T, in hours.
Do you mean:

$Evan:C=80\left(\frac12\right)^{\frac12 \bold{\color{red}T}}$

$Chelsea:C=40\left(\frac12\right)^{\frac13\bold{\co lor{red} T}}$

The exponents are actually 1/2 and 1/3 respectively, I'm not sure how to show a fraction in the exponent here.

A.) Who had to take the higher dosage. Explain.
B.) Whose system got rid of the medication at a faster rate? Explain.
...

3. Sorry about the confusion there, fractions were a bit small in the book so it looked like there were 1's in the exponent numerators,it's actually t/2 and t/3:

should be: $Evan: C=80\frac{1}{2}^\frac{t}{2}$

With brackets around the 1/2 of course, couldn't figure out how to put in brackets without getting an error.

The 2nd one should be:

$C=40\frac{1}{2}^\frac{t}{3}$

Again with the brackets around the 1/2

4. Originally Posted by Vesicant
Sorry about the confusion there, fractions were a bit small in the book so it looked like there were 1's in the exponent numerators,it's actually t/2 and t/3:
Actually your (new) notation and my notation are exactly the same.

If you want to know how to write large brackets just click on one of the equations I've posted previously: You'll get the code which you have to use in a separate window.

Originally Posted by Vesicant
Just been having a little problem with this one, was hoping you guys could point me in the right direction:

Evan and Chelsea are given the same medication. However, due to their different weights and metabolic rates the dosages and the rates at which the medication leaves their systems are different. The following functions describe the concentration of medicine in their blood streams,C, with respect to time, T, in hours.

$Evan:C=80\left(\frac12\right)^{\frac12}$ $Chelsea:C=40\left(\frac12\right)^{\frac13}$

The exponents are actually 1/2 and 1/3 respectively, I'm not sure how to show a fraction in the exponent here.

A.) Who had to take the higher dosage. Explain.
...
That depends: You can show that the concentration of the medicine is higher in Evan's blood if $0 < T < 6$

and it is higher in Chelsea's blood for $T > 6$

So in my opinion this question can't be answered unambiguously.

To answer the 2nd question calculate the drivative of the functions and determine the one whose gradient is larger then the other one.