Question

Haley conducted a study which found that a cup of coffee contains 150 milligrams of caffeine. the amount of caffeine in the body each hour after consumption of one cup is 9% less than the previous hour. if haley conducted her study for a total of 10 hours, which inequality represents the range of the exponential function that models this situation?

Answer 1

$58.41 < f(x) < 150$ inequality represents the range of the exponential function that models this situation

The exponential decay function is as follows:

$y = a(1-r)^t$

Here,

y = final value

a = initial value

r = decay rate

t = time taken

Given that:

a = 150 mg

r = 9% = 0.09

Then the next hour the amount of caffeine in the body will be:

$y = a (1-r)^t\\y = 150 \times (1-0.09)^2$ = 136.5

Similarly, after 10 hours the amount of caffeine in the body will be:

$y = 150 \times (1- 0.09)^{10} = 58.41$

Then the inequality representing the range of the exponential function that models this situation is:

58.41 < f(x) < 150

To learn more about inequality with the given link

https://brainly.com/question/20383699

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