Given:
An adult takes 800 mg of ibuprofen.
Each hour, one fourth of the medicine leaves the system.
To find:
The exponential equation that models this situation.
Solution:
The general exponential model is
[tex]y=a(1-r)^x[/tex] ...(i)
where, a is initial value r is decreasing rate and x is time period.
According to the question,
Initial value of medicine = 800 mg
Decreasing at the rate of [tex]\dfrac{1}{4}[/tex] per hour.
Putting a=800 and [tex]r=\dfrac{1}{4}[/tex] in (i), we get
[tex]y=800(1-\dfrac{1}{4})^x[/tex]
[tex]y=800(\dfrac{4-1}{4})^x[/tex]
[tex]y=800(\dfrac{3}{4})^x[/tex]
Therefore, the required exponential equation that models the given situation is [tex]y=800(\dfrac{3}{4})^x[/tex], where, y is ibuprofen (in mg) after x hours.
