Question

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

Answer 1

Important:  f(x)=40,000(0.75)x   should be written  f(x)=40,000(0.75)^x.
                                                          f(b) - f(a)
The average rate of change (arc) is --------------
                                                             b - a

Here that comes to 40000 [0.75^5 - 0.75^2]
                                --------------------------------
                                            5-2

or    arc = -13007.81 / 3  = -4335.9 bacteria per year.