Question

Determine whether the statement is true or false. Suppose P(t) represents the population of bacteria at time t and suppose P'(t) > 0 and P''(t) < 0; then the population is increasing at time t but at a decreasing rate. True

Answer 1

TRUE

Step-by-step explanation:

If the population follows a logistic growth curve, the graph of P vs t will look like the diagram below.

The rate of growth (P') increases slowly at first, then increases rapidly from 2 to 4, and then slows down, but always P > 0.

The graph has an inflection point at (3, 1000). That's the point at which the rate of growth starts slowing down.

When t < 3, P'' > 0.

When t = 3, P'' = 0.

When t > 3, P'' < 0, because the rate of population growth is slowing down.

Thus, if the population is in the final phase of logistic growth, the population is increasing at a decreasing rate (TRUE)..