Question

The number of milligrams D (h) of a drug in a patient's bloodstream h hours after the drug is injected is modeled by the following function.D(h) = 50e-0.5hFind the initial amount injected and the amount in the bloodstream after 7 hours.Round your answers to the nearest hundredth as necessary.

Answer 1

This is a "rounding problem". The population size after 6 years is P(6):

$P(6)=\frac{450}{1+8\cdot e^{-0.29\cdot(6)}}\approx187.175$

Now, for the first decimal place (1) is less than 5, 187.175 becomes 187 (by the rounding rule); namely,

$P(6)\approx187$

On the other hand, the population size after 8 years is P(8):

$P(8)=\frac{450}{1+8\cdot e^{-0.29\cdot(8)}}\approx251.93$

Now, for the first decimal place (9) is greater than 5, 251.93 becomes 252; namely,

$P(8)\approx252$