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Well $40\% \times 1 g = 400 \space mg$ That's how much drug is in your body's fluid compartments.

If the drug's half-life is $12$ hrs, the amount of drug in your body (after $24$ hrs) = $\frac{1}{2} \times \frac{1}{2} \times 400 = 100 \space mg$.

If dose = $d$ and bioavailability = $b\%$ and half-life = $h$ hours ...

The amount of drug left in your body after $t$ hrs = $\left(\frac{1}{2}\right)^{\frac{t}{h}} \times b\% \times d$

EDIT 1 START

This fancy geometric/mixed (?) series might be of interest ...

$1 - \left(1 \times \left(\frac{1}{2}\right) + \frac{3}{2} \times \left(\frac{1}{2}\right)^2 + ... \right) = 0$ where $1$ = bioavailability.

EDIT 1 END

Well $40\% \times 1 g = 400 \space mg$ That's how much drug is in your body's fluid compartments.

If the drug's half-life is $12$ hrs, the amount of drug in your body (after $24$ hrs) = $\frac{1}{2} \times \frac{1}{2} \times 400 = 100 \space mg$.

If dose = $d$ and bioavailability = $b\%$ and half-life = $h$ hours ...

The amount of drug left in your body after $t$ hrs = $\left(\frac{1}{2}\right)^{\frac{t}{h}} \times b\% \times d$

EDIT 1 START

This fancy geometric/mixed (?) series might be of interest ...

$1 - \left(1 \times \left(\frac{1}{2}\right)^1 + \frac{3}{2} \times \left(\frac{1}{2}\right)^2 + ... \right) = 0$ where $1$ = bioavailability, the exponent is $\frac{t}{h}$ and the rate of drug absorption = $1$/hr.

EDIT 1 END

Well $40\% \times 1 g = 400 \space mg$ That's how much drug is in your body's fluid compartments.

If the drug's half-life is $12$ hrs, the amount of drug in your body (after $24$ hrs) = $\frac{1}{2} \times \frac{1}{2} \times 400 = 100 \space mg$.

If dose = $d$ and bioavailability = $b\%$ and half-life = $h$ hours ...

The amount of drug left in your body after $t$ hrs = $\left(\frac{1}{2}\right)^{\frac{t}{h}} \times b\% \times d$

EDIT 1 START

This fancy geometric series might be of interest ...

$1 \times \left(\frac{1}{2}\right) + \frac{3}{2} \times \left(\frac{1}{2}\right)^2 + ...$

EDIT 1 END

Well $40\% \times 1 g = 400 \space mg$ That's how much drug is in your body's fluid compartments.

If the drug's half-life is $12$ hrs, the amount of drug in your body (after $24$ hrs) = $\frac{1}{2} \times \frac{1}{2} \times 400 = 100 \space mg$.

If dose = $d$ and bioavailability = $b\%$ and half-life = $h$ hours ...

The amount of drug left in your body after $t$ hrs = $\left(\frac{1}{2}\right)^{\frac{t}{h}} \times b\% \times d$

EDIT 1 START

This fancy geometric/mixed (?) series might be of interest ...

$1 - \left(1 \times \left(\frac{1}{2}\right) + \frac{3}{2} \times \left(\frac{1}{2}\right)^2 + ... \right) = 0$ where $1$ = bioavailability.

EDIT 1 END

Well $40\% \times 1 g = 400 \space mg$ That's how much drug is in your body's fluid compartments.

If the drug's half-life is $12$ hrs, the amount of drug in your body (after $24$ hrs) = $\frac{1}{2} \times \frac{1}{2} \times 400 = 100 \space mg$.

If dose = $d$ and bioavailability = $b\%$ and half-life = $h$ hours ...

The amount of drug left in your body after $t$ hrs = $\left(\frac{1}{2}\right)^{\frac{t}{h}} \times b\% \times d$

Well $40\% \times 1 g = 400 \space mg$ That's how much drug is in your body's fluid compartments.

If the drug's half-life is $12$ hrs, the amount of drug in your body (after $24$ hrs) = $\frac{1}{2} \times \frac{1}{2} \times 400 = 100 \space mg$.

If dose = $d$ and bioavailability = $b\%$ and half-life = $h$ hours ...

The amount of drug left in your body after $t$ hrs = $\left(\frac{1}{2}\right)^{\frac{t}{h}} \times b\% \times d$

EDIT 1 START

This fancy geometric series might be of interest ...

$1 \times \left(\frac{1}{2}\right) + \frac{3}{2} \times \left(\frac{1}{2}\right)^2 + ...$

EDIT 1 END