Question

!!!PLEASE ANSWER, ASAP!!!An adult takes 800 mg of ibuprofen. Each hour, one fourth of the medicine leaves the system. Write the exponential equation that models this situation.

Answer 1

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

`y=a(1-r)^x` ...(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
`(1)/(4)` per hour.

Putting a=800 and
`r=(1)/(4)` in (i), we get

`y=800(1-(1)/(4))^x`

`y=800((4-1)/(4))^x`

`y=800((3)/(4))^x`

Therefore, the required exponential equation that models the given situation is
`y=800((3)/(4))^x`, where, y is ibuprofen (in mg) after x hours.