Question

WILL GIVE BRAINLIEST
If a hospital patient is given 100 milligrams of medicine which leaves the bloodstream at 14% per hour, how many milligrams of medicine will remain in the system after 10 hours? Use the function A(t) = Iert.
24.66 mg
86.94 mg
90.48 mg
405.52 mg

Answer 1

All you have to do is plug in the given values into the given equation and evaluate.

The expression is,

$A(t) = l{e}^{rt}$
But we have to analyze the problem carefully. This is a natural phenomenon that can be modelled by a decay function. The reason is that, after every hour we expect the medicine in the blood to keep reducing.

Therefore we use the decay function rather. This is given by,


$A(t) = l{e}^{-rt}$

where,

$l = 100 \: milligrams$

$r = \frac{14}{100} = 0.14$

and

$t = 10 \: hours$

On substitution, we obtain;

$A(10) = 100 \times {e}^{ - 0.14 \times 10}$


$A(10) = 100 \times {e}^{ - 1.4}$



Now, we take our calculators and look for the constant
$e$

,then type e raised to exponent of -1.4. If you are using a scientific or programmable calculator you will find this constant as a secondary function. Remember it is the base of the Natural logarithm.



If everything goes well, you should obtain;

$A(10) = 100 \times 0.24659639$


This implies that,


$A(10) = 24.66$

Therefore after 10 hours 24.66 mg of the medicine will still remain in the system.