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[tex]58.41 < f(x) < 150[/tex] inequality represents the range of the exponential function that models this situation
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
Given 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\\y = 150 \times (1-0.09)^2[/tex] = 136.5
Similarly, after 10 hours the amount of caffeine in the body will be:
[tex]y = 150 \times (1- 0.09)^{10} = 58.41[/tex]
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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