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.

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

      ...(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 per hour.

Putting a=800 and in (i), we get

Therefore, the required exponential equation that models the given situation is , where, y is ibuprofen (in mg) after x hours.

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .