# A serving of a popular cola soft drink has 46 mg of caffeine. Suppose the half-life for caffeine remaining in he body of a typical adult is 6 h. How do you write an exponential decay function that gives the amount of caffeine in the body after t hours?

##### 1 Answer

Nov 27, 2017

See below.

#### Explanation:

We need an equation of the form:

Where

To find the the constant

We know the half life is 6 hours, so after 6 hours the amount

So:

Solve for

Taking natural logs of both sides:

So our equation is:

This could also be written:

TEST:

Graph of