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vaieri [72.5K]
3 years ago
8

Select the correct answer.

Mathematics
1 answer:
castortr0y [4]3 years ago
6 0

Answer:

The correct option is (B)58.41.

Step-by-step explanation:

The exponential decay function is as follows:

y=a(1-r)^{t}

Here,

<em>y = </em>final value

<em>a</em> = initial value

<em>r</em> = decay rate

<em>t</em> = time taken

It is provided that:

<em>a = </em>150 mg

<em>r</em> = 9% = 0.09

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

y=a(1-r)^{t}\\=150\times (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\times (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\times (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

Thus, the correct option is (B).

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