Let F(t) represent the average rate of change in the growth of bacteria with respect to time (t) in hours.

Let ƒ(t) represent the amount of bacteria in the sample at time t.

At time t_{1}= 1 hour, the amount of bacteria in the sample is ƒ(t_{1}) = ƒ(1) = 250

At time t_{2}= 3 hours, the amount of bacteria in the sample if ƒ(t_{2}) = ƒ(3) = 1000

The average rate of change is represented by the following formula:

F(t) = [ƒ(t_{2}) - ƒ(t_{1})] / (t_{2} - t_{1})

= [ƒ(3) - ƒ(1)] / (3-1)

= (1000 - 250) / (2)

= (750) / (2)

F(t) = 375

Thus, the average rate of the growth of the bacteria in the sample is 375. That is, the amount of bacteria in the sample is increasing/growing at a rate of 375 bacteria per hour.