Question

question 2 of 5
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?

• ( 0 leq f(x) leq 10 )
• ( 150 leq f(x) leq 355.1 )
• ( 0 leq f(x) leq 150 )
• ( 58.41 leq f(x) leq 150 )

Explanation:

Step1: Define exponential decay function

The initial amount of caffeine is 150 mg, and each hour it is 91% (100% - 9%) of the previous amount. The function is:
$$f(x) = 150(0.91)^x$$
where $x$ is the number of hours, $0 \leq x \leq 10$.

Step2: Find maximum value of $f(x)$

The maximum occurs at $x=0$ (initial time):
$$f(0) = 150(0.91)^0 = 150$$

Step3: Find minimum value of $f(x)$

The minimum occurs at $x=10$ (10 hours later):
$$f(10) = 150(0.91)^{10} \approx 150 \times 0.3894 = 58.41$$

Answer:

D. $58.41 \leq f(x) \leq 150$