QQuestionMathematics
QuestionMathematics
f(x)= 9,000(0.66)^{x}
The given function $f$ models the number of advertisements a company sent to its clients each year, where $x$ represents the number of years since 1997, and $0 \leq x \leq 5$. If $y=f(x)$ is graphed in the $x y$-plane, which of the following is the best interpretation of the $y$-intercept of the graph in this context?
A. The minimum estimated number of advertisements the company sent to its clients during the 5 years was 1,708 .
B. The minimum estimated number of advertisements the company sent to its clients during the 5 years was 9,000 .
C. The estimated number of advertisements the company sent to its clients in 1997 was 1,708 .
D. The estimated number of advertisements the company sent to its clients in 1997 was 9,000 .
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Answer
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Step 1:: Identify the y-intercept of the given function.
f(0)=9,000(0.66)^{0}=9,000 \times 1=9,000
Step 2:: Interpret the y-intercept in the context of the problem.
The y-intercept represents the estimated number of advertisements the company sent to its clients in 1997, as $x$ represents the number of years since 1997.
Step 3:: Compare the calculated y-intercept with the given answer choices.
The estimated number of advertisements the company sent to its clients in 1997 is 9,000, which matches option D.
Final Answer
The estimated number of advertisements the company sent to its clients in 1997 was 9,000.
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