Basic functions: Power functions
Computing the equivalent dose of antipsychotics
Use in this exercise the power relationship of the form \[y=c\cdot x^b\] where \(y\) the dose of a given antipsychotic, \(x\) is the equivalent dose of chlorpromazine (CPZ) or the equivalent dose of haloperidol (HPD), and \(b\) and \(c\) drug-specific, experimentally determined numbers for the two reference antipsychotics.
| Antipsychotic | relationship (\(x={}\)CPZ dose) | relationship (\(x={}\)HPD dose) |
| clozapine | \(\quad y=2.027\,x^{0.864}\) | \(\quad y=66.58\,x^{0.796}\) |
| risperidone | \(\quad y=0.019\,x^{0.924}\) | \(\quad y=0.790\,x^{0.851}\) |
| olanzapine | \(\quad y=0.086\,x^{0.870}\) | \(\quad y=2.900\,x^{0.805}\) |
| quetiapine | \(\quad y=2.806\,x^{0.852}\) | \(\quad y=88.16\,x^{0.786}\) |
| aripiprazole | \(\quad y=0.255\,x^{0.700}\) | \(\quad y=4.343\,x^{0.645}\) |
| chlorpromazine | \(\quad y=x\) | \(\quad y=56.98\,x^{0.923}\) |
| haloperidol | \(\quad y=0.013\,x^{1.082}\) | \(\quad y=x\) |
A patient uses \(50\,\mathrm{mg}\) quetiapine and \(5\,\mathrm{mg}\) aripiprazol daily.
What is the equivalent dose of chlorpromazine, in mg and rounded to 2 decimal places?
| Equivalent CPZ dose = | in mg and rounded to 2 decimal places. |
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