A function models the number of bacteria (in millions) in a culture
MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
A function g models the number of bacteria (in millions) in a culture. Its derivative g′(t), measured in millions of bacteria per hour, is negative for every t in the interval 2≤t≤5. Which of the following statements is most accurate about the culture during that time interval?
(a) The number of bacteria increased over that interval because g′(t)=0 for all t in [2,5].
(b) The number of bacteria stayed approximately constant since the positive and negative changes in g′(t) would balance out over the entire interval.
(c) The number of bacteria decreased over that interval because ∫25g′(t)dt<0.
(d) The available information is insufficient; without the exact values of g′(t) we cannot tell whether the population increased or decreased.