# Thread: Linear Equation

1. ## Linear Equation

Pharmacological products must specify recommended dosages for adults and children. Two formulas for modification of adult dosages levels for young children are

Cowling's rule: y = (1 / 24) (t + 1)a
Friend's rule: y = (2 / 25)ta

where a denotes the adult dose (in milligrams) and t denotes the age of the child (in years).

(a) If a = 100, graph the two linear equations on the same axes for 0 <= t <= 12.

(b) For what age do the two formulas specify the same dosage?

2. ## Re: Linear Equation

Well have you graphed the functions yet?

3. ## Re: Linear Equation

I got 2 parallel Lines.

First Equation
t 0 1 2
y 25/6 25/3 25/2

Second Equation
t 0 1 2
y 0 8 16

4. ## Re: Linear Equation

Hi

I would tackle the graph plotting by taking t = 0 and t = 12 and calculate the yc and yf values as below -

t : 0 12
yc : 25/6 25.13/6 (this is < 72 so these lines must cross)
yf : 0 72

I don't think these are actually parallel although they may look so over a smaller range.

Regards

5. ## Re: Linear Equation

Originally Posted by joshuaa
I got 2 parallel Lines.

First Equation
t 0 1 2
y 25/6 25/3 25/2

Second Equation
t 0 1 2
y 0 8 16
$a=100$

$y_c(t)=y_f(t)$

$\dfrac {100(t+1)}{24}=\dfrac{200 t}{25}$

$2500(t+1)=4800t$

$2500=2300t$

$t=\dfrac {25}{23}$

not really that big a deal

6. ## Re: Linear Equation

Thank You. It was helpful.