Answer:
The correct option is (B)[tex]58.41<f(x)<150[/tex].
Step-by-step explanation:
The exponential decay function is as follows:
[tex]y=a(1-r)^{t}[/tex]
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:
[tex]y=a(1-r)^{t}\\=150\times (1-0.09)^{1}\\=136.5\ \text{mg}[/tex]
Then after two hours the amount of caffeine in the body will be:
[tex]y=a(1-r)^{t}\\=150\times (1-0.09)^{2}\\=124.215\ \text{mg}[/tex]
Similarly after 10 hours the amount of caffeine in the body will be:
[tex]y=a(1-r)^{t}\\=150\times (1-0.09)^{10}\\=58.4124\ \text{mg}\\\approx 58.41\ \text{mg}[/tex]
Then the inequality representing the range of the exponential function that models this situation is:
[tex]58.41<f(x)<150[/tex]
Thus, the correct option is (B).
