Let represent the instantaneous growth rate

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Let

g(t)=\dfrac{5}{t-3}

represent the instantaneous growth rate, in hundreds of bacteria per minute, of a culture for

t>3

minutes. Which of the following best interprets the statement

\displaystyle \lim_{t\to 3^{+}} g(t)=\infty

in the context of the culture? (a) The growth rate decreases without bound as time approaches

3

minutes from the right. (b) The growth rate stabilizes at

5

hundreds of bacteria per minute as

t

approaches

3

minutes. (c) As time approaches

3

minutes from the right, the growth rate becomes increasingly large without bound. (d) The number of bacteria becomes infinitely large exactly at

t=3

minutes.