If y=a^{x}, what does x equal?

x=log_{a}y

If y=10^{x} , what does x equal?

x=logy

How do you figure out what log_{2}8 is?

Figure out what power 2 needs to be put to in order to equal 8

i.e. 3

What does log_{a}xy equal?

log_{a}x+log_{a}y

What does log_{a}x/y equal?

log _{a}x-log _{a}y

What does log_{a}x^{r }equal?

rlog_{a}x

What does log_{a}a equal?

1

What does log_{a}1 equal?

0

What does log_{a}x+log_{a}y equal?

log_{a}xy

What does log_{a}x-log_{a}y equal?

log_{a}x/y

What does rlog_{a}x equal?

log_{a}x^{r}

How would you make the line y=cx^{k }linear?

Using a log-log scale

If y=cx^{k} , what does logy equal?

logc+klogx

What is common log?

Log base 10 (log_{10})

If y=e^{x}, what does x equal?

lny

How else can lny be represented?

log_{e}y

What does e equal (to 3 decimal places?

2.718

How would you make the line y=ce^{ kx } linear?

Using a log-linear scale

If y=ce^{kx} , what does lny equal?

lnc+kx

If y(t)=y_{0}e^{kt}, and k>0, what will the curve look like?

It will be exponentially growing

If y(t)=y0e^{-kt}, and k>0, what will the curve look like?

It will be decreasing at a slowing rate

What is biological half-life also called?

Elimination half-life

What is biological half-life?

The time it takes for a substance to lose one‐half of its pharmacological, physiological, or radiological activity.

What is the formula for biological half-life?

t_{1/2}=ln2/k

Give a simple mathematic pharmacokinetic elimination model

C=C_{0}e^{-Kt} for t≥0, K>0

Where:

- C denotes the plasma/serum drug concentration at time t (measured in mass/volume; e.g. mg/mL);
- C
_{0}denotes the initial plasma/serum drug concentration - K denotes the elimination rate constant (measured in reciprocal time; e.g. h
^{‐1}, min^{‐1}, s^{‐1}) - t denotes time (e.g. hours, minutes, seconds).

If C=C_{0}e^{-Kt}, what does lnC equal?

lnC = ln(C_{0})-Kt

What is termination of action?

The time at which the drug concentration in the plasma/serum falls below the minimum level of the therapeutic range.

What is the formula for a logistic function?

y=L/(1+ae^{-kt})

Where L=carrying capacity

L/2=the inflection point

How will k effect a logistic model?

A large k will show a large surge in the data, a small k will show a gradual rise

What does a dose-response curve plot?

The intensity (usually scaled as a percentage of the maximum response) of physiological response to a drug as a function of the dose administered.