Question

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Ted just finished his morning cup of coffee, which contained 190 milligrams of caffeine. The amount of caffeine in his system should decrease by about 13% each hour. You can use a function to approximate the amount of caffeine that will remain in Ted's system x hours from now.
Is the function linear or exponential?

Answer 1

Exponential.

Because the caffeine decreases by a fixed percentage (13%) each hour, the amount after x hours is modeled by
f(x) = 190(0.87)^x,
which is an exponential decay function (not linear, since the change per hour is multiplicative, not a constant additive amount).