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AP Precalculus -2.5 Exponential Function Modeling- MCQ Exam Style Questions - Effective Fall 2023

AP Precalculus -2.5 Exponential Function Modeling- MCQ Exam Style Questions – Effective Fall 2023

AP Precalculus -2.5 Exponential Function Modeling- MCQ Exam Style Questions – AP Precalculus- per latest AP Precalculus Syllabus.

AP Precalculus – MCQ Exam Style Questions- All Topics

Question 

Water hyacinth is an invasive plant species found in many lakes that typically grows at a rate of 7% per day. As part of a study, a scientist introduces a 150-gram sample of water hyacinth into a testing pool. Which of the following functions gives the amount of water hyacinth in the testing pool \( t \) weeks after the sample is introduced? (Note: 1 week is 7 days.)
(A) \( f(t) = 150 \left( 1 + 0.07^{(1/7)} \right)^t \)
(B) \( g(t) = 150 \left( 1.07^{(1/7)} \right)^t \)
(C) \( h(t) = 150 \left( 1 + 0.07^{(7)} \right)^t \)
(D) \( k(t) = 150 \left( 1.07^{(7)} \right)^t \)
▶️ Answer/Explanation
Detailed solution

Daily growth factor: \( 1 + 0.07 = 1.07 \).
In one week (7 days), growth factor = \( (1.07)^7 \).
If \( t \) is in weeks, amount after \( t \) weeks: \( 150 \cdot (1.07^7)^t = 150 \cdot (1.07)^{7t} \).
The given options:
(D) \( k(t) = 150 (1.07^{(7)})^t = 150 \cdot (1.07^7)^t \), matches.
✅ Answer: (D)

Question 

The sales of a new product, in items per month, is modeled by the expression \( 225 + 500 \log_{10}(15t + 10) \), where \( t \) represents the time since the product became available for purchase, in months. What is the number of items sold per month for time \( t = 6 \)?
(A) 725
(B) 1225
(C) 1700
(D) 5225
▶️ Answer/Explanation
Detailed solution

Plug \( t = 6 \):
\( 15t + 10 = 15(6) + 10 = 90 + 10 = 100 \)
\( \log_{10}(100) = 2 \)
Sales = \( 225 + 500 \times 2 = 225 + 1000 = 1225 \)
✅ Answer: (B)

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