Question

Bacteria is growing in a petri dish in such a way that the population of bacteria at time t in minutes is defined by the function P(t)=2t 3 +t+2,t≥0. Include units in your final answer. a. Find the average rate of change of the bacteria population from t=0 to t=3 minutes. [3] b. Find the instantaneous rate of change of the bacteria population at t=2 minutes.

Answer 1

The average rate of change of the bacteria population from t=0 to t=3 minutes is 19 bacteria per minute.

Step-by-step explanation:

To find the average rate of change of the bacteria population from t=0 to t=3 minutes, we need to find the difference in the population at t=0 and t=3, and divide it by the difference in time.

Using the function P(t)=2t^3 + t + 2, we substitute t=0 to find the initial population: P(0) = 2(0)^3 + 0 + 2 = 2.

Next, we substitute t=3 to find the population at t=3: P(3) = 2(3)^3 + 3 + 2 = 59.

The difference in population is 59 - 2 = 57, and the difference in time is 3 - 0 = 3.

Therefore, the average rate of change of the bacteria population from t=0 to t=3 minutes is 57/3 = 19 bacteria per minute.