1. ## continuity...any help?

A 0.5 ml dose of a drug is injected into a patient steadily for one second. At the end of this time, the quantity, Q, of the drug in the body starts to decay exponentially at a continuous rate of 0.3 % per second. Express Q as a continuous function of t.

Q(t)= A, 0 < or = to t < or = to 1
B, 1<t

A(t)=

B(t)=

2. Originally Posted by mer1988
A 0.5 ml dose of a drug is injected into a patient steadily for one second. At the end of this time, the quantity, Q, of the drug in the body starts to decay exponentially at a continuous rate of 0.3 % per second. Express Q as a continuous function of t.

Q(t)= A, 0 < or = to t < or = to 1
B, 1<t

A(t)=

B(t)=
Hello,

the general form of the equation which describes exponential decay is:

$\displaystyle A(t)=a_0 \cdot e^{k \cdot t}$
$\displaystyle A(t)$ is the amount at the time t
$\displaystyle A_0$ is the initial amount
k isa constant factor which spcify the speed of decaying(?)

You know that there are left only 0.4985 ml after the first second. This allows us to calculate the constant k:

$\displaystyle 0.4985 \ ml = 0.5\ ml \cdot e^{k \cdot 1}$ will give $\displaystyle k \approx -0.00300451$

Therefore the equation of the function is:

$\displaystyle Q(t) = 0.5 \cdot e^{-0.00300451 \cdot t}$

As you may have noticed $\displaystyle k \approx -0.3\ \%$. You can only use this property for small values of k.