Question

A patient is given a 50 mg dose of medicine the medicines effectiveness decreases every hour at a constant rate of 40% what is the exponential decay function that models this scenario how much medicine will be left in the patient's system after two hours

Answer 1

Exponential decay formula is
$y = a(1 - r)^{x} \\ y = 50(1 - .40) ^{x}$
x= hours past
$y = 50(1 - .40)^{2} \\ y = 18$
after 2 hours, there are 18 mg of medicine left

Answer 2

Answer:

$A=50(0.6)^x$

18 mg of medicine will be left in the patient's system after two hours.

Step-by-step explanation:

Given,

The initial quantity of the medicine, P = 50 mg,

Also, it decreases every hour at a constant rate of 40%

That is, r = 40 %,

Thus, the quantity of the medicine after x hours,

$A=P(1-\frac{r}{100})^r$

$=50(1-\frac{40}{100})^x$

$=50(1-0.4)^x$

$=50(0.6)^x$

Which is the required exponential decay function that models this scenario.

The quantity of the medicine after 2 hours,

$A=50(0.6)^2=18\text{ mg}$