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

`A=50(0.6)^x`

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

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-(r)/(100))^r`

`=50(1-(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}`