Question

Select the correct answer.

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?
150 s f(x) s 355.1
58.41 s f(x) < 150
O s f(x) s 10
0 <f(x) s 150
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Answer 1

The best answer's you can get are the already answered one's (posted cause a guy in the comment said it was wrong when it was actually correct)

Answer 2

The correct option is (B)
`58.41<f(x)<150`.

Explanation:

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

It is provided 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)\\=150* (1-0.09)^(1)\\=136.5\ \text{mg}`

Then after two hours the amount of caffeine in the body will be:

`y=a(1-r)^(t)\\=150* (1-0.09)^(2)\\=124.215\ \text{mg}`

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

`y=a(1-r)^(t)\\=150* (1-0.09)^(10)\\=58.4124\ \text{mg}\\\approx 58.41\ \text{mg}`

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

`58.41<f(x)<150`

Thus, the correct option is (B).