Irene just drank a cup of coffee to help her stay awake. The coffee had 120 milligrams of caffeine in it. If her body processes 10% of the caffeine every hour, how much will be left in 10 hours? If necessary, round your answer to the nearest tenth.

Hi there!

For this, we need to use an exponential function. This is because it constantly takes 10% of what is left, not just 10% of the total. The formula for an exponential function:

Where is the original value, is the rate of change, and is the time. We know the original value is 120 milligrams. The rate of change is 90%, as after every hour there is 90% of what there was previously remaining. Finally, we are looking for how much is remaining after 10 hours, so 10 is the time.

Plugging this all in, we get:

Now, solving:

Thus, after rounding, we get that 41.8 milligrams of caffeine will be left in 10 hours.

Hope this helps! Feel free to let me know if you have additional questions about this problem.