The function f(x)=40,000(0.75)x represents the number of bacteria present in a petri dish after x hours. What is the average rate of change in the number of bacteria between Hour 2 and Hour 5?
Question 1 options:
A.−6102 bacteria/h
B.4336 bacteria/h
C.−4336 bacteria/h
D.6102 bacteria/h

The average rate of change in the number of bacteria between Hour 2 and Hour 5 is approximately -3,482 bacteria/hour.

To find the average rate of change in the number of bacteria between Hour 2 and Hour 5, we need to calculate the difference in the number of bacteria at Hour 5 and Hour 2, and then divide it by the difference in time (3 hours).

At Hour 2, substitute x = 2 into the function f(x) = 40,000(0.75)^x:

f(2) = 40,000(0.75)^2 = 40,000(0.5625) = 22,500 bacteria.

At Hour 5, substitute x = 5 into the function:

f(5) = 40,000(0.75)^5 = 40,000(0.3164) = 12,656 bacteria.

Now we can calculate the average rate of change:

Average rate of change = (f(5) - f(2)) / (5 - 2) = (12,656 - 22,500) / 3 = -3,482 bacteria/hour. The average rate of change in the number of bacteria between Hour 2 and Hour 5 is approximately -3,482 bacteria/hour.

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