Question

A doctor prescribes 150 milligrams of a therapeutic drug that decays by about 15% each hour. To the nearest hour, what is the half-life of the drug?

Answer 1

Answer:

4 hours

Step-by-step explanation:

The amount remaining at the end of each hour is 0.85 of the amount at the start of the hour. You want to find the exponent such that ...

... 0.85^x = 0.5 . . . . . x = the number of hours until half is left

... x·log(0.85) = log(0.5) . . . . . take the log to turn it to a linear equation

... x = log(0.5)/log(0.85) ≈ 4.265024

Rounded to the nearest  hour, x = 4.