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AP Precalculus -2.6 Competing Function Models- MCQ Exam Style Questions - Effective Fall 2023

AP Precalculus -2.6 Competing Function Models- MCQ Exam Style Questions – Effective Fall 2023

AP Precalculus -2.6 Competing Function Models- MCQ Exam Style Questions – AP Precalculus- per latest AP Precalculus Syllabus.

AP Precalculus – MCQ Exam Style Questions- All Topics

Question 

 
 
 
 
 
 
 
 
 
 
A food vendor developed a new sandwich type for sale. The vendor made estimates about the sales of the new sandwich type over time. A linear regression was used to develop a model for the sales over time. The figure shows a graph of the residuals of the linear regression. Which of the following statements about the linear regression is true?
(A) The linear model is not appropriate, because there is a clear pattern in the graph of the residuals.
(B) The linear model is not appropriate, because the graph of the residuals has more points above 0 than below 0.
(C) The linear model is appropriate, because there is a clear pattern in the graph of the residuals.
(D) The linear model is appropriate, because the positive residual farthest from 0 and the negative residual farthest from 0 are about the same distance, although more points are above 0 than below 0.
▶️ Answer/Explanation
Detailed solution

If residuals show a clear pattern (curved shape, systematic deviation), the linear model is not appropriate.
From the description/figure (not shown here), residuals likely show a pattern.
✅ Answer: (A)

Question 

The increasing function \( P \) gives the number of followers, in thousands, for a new musical group on a social media site. The table gives values of \( P(t) \) for selected values of \( t \), in months, since the musical group created their account on this social media site.
\( t \) (months)01234
\( P(t) \) (thousands)20304567.5101.25
If a model is constructed to represent these data, which of the following best applies to this situation?
(A) \( y = 10t + 20 \)
(B) \( y = \frac{325}{16} t + 20 \)
(C) \( y = 20\left(\frac{2}{3}\right)^t \)
(D) \( y = 20\left(\frac{3}{2}\right)^t \)
▶️ Answer/Explanation
Detailed solution

Observe the ratios of consecutive outputs:
\( 30/20 = 1.5 \), \( 45/30 = 1.5 \), \( 67.5/45 = 1.5 \), \( 101.25/67.5 = 1.5 \).
Constant ratio \( 1.5 = \frac{3}{2} \) indicates exponential growth: \( P(t) = a \cdot \left(\frac{3}{2}\right)^t \).
Using \( P(0) = 20 \) gives \( a = 20 \).
Thus \( P(t) = 20\left(\frac{3}{2}\right)^t \).
✅ Answer: (D)

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