AP Calculus BC : 5.11 Solving Optimization Problems- Exam Style questions with Answer- MCQ

Question 

Bacteria in a certain culture increase at a rate proportional to the number present. If the number of
bacteria doubles in three hours, in how many hours will the number of bacteria triple?
(A) \(\frac{3ln 3}{ln 2}\)           (B) \(\frac{2ln 3}{ln 2}\)                      (C)\( \frac{ln 3}{ln 2}\)               (D) \(ln\left ( \frac{27}{2} \right )\)                  (E)\(ln\left ( \frac{27}{2} \right ) \)

Answer/Explanation

Ans:A

Question 

What is the area of the largest rectangle that can be inscribed in the ellipse \(4x^{2}+9y^{2}=36\)
(A) \(\sqrt[6]{2}\)                              (B) 12                              (C) 24                                     (D) \(\sqrt[24]{2}\)                                     (E) 36

Answer/Explanation

Ans:B

Question

 The position of an object attached to a spring is given by \(y(t)=\frac{1}{6}cos(5t)-\frac{1}{4}sin(5t) \), where t is time in seconds. In the first 4 seconds, how many times is the velocity of the object equal to 0?
(A) Zero

(B) Three

(C) Five

(D) Six

(E) Seven

Answer/Explanation

 

Question

Consider all right circular cylinders for which the sum of the height and circumference is 30 centimeters. What is the radius of the one with maximum volume?

(A) 3 cm                        (B) 10 cm                          (C) 20 cm                                     (D) \(\frac{30}{π^{2}}cm\)                                  (E) \(\frac{10}{π}cm\)

Answer/Explanation

Ans:E

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