Question

Select the correct answer.

Answer 1

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,

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:

$y=a(1-r)^{t}\\=150\times (1-0.09)^{1}\\=136.5\ \text{mg}$

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).