## 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 c

Question

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.

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2 weeks 2021-09-08T20:32:19+00:00 1 Answer 0

1. 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.