# determine the average rate of change for the number of bacteria and the rate at which the colony is increasing time in days  0          1,         2,         3,          4,          5,              6, Population  50,      153,     234,      357,       547,       839,           1280 a) determine the average rate of change for the number of bacteria over the 6 day period. b) estimate the rate at which the colony is increasing at day 2 . The average rate of change is

= (Final bacterial count - Initial Count)/(total time)

The average rate of change = (1280-50)/6

= 205 bacteria per day.

To find the rate of increase of colony, the most sitable method is to use the central derivative approximation formula.

The central derivative...

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The average rate of change is

= (Final bacterial count - Initial Count)/(total time)

The average rate of change = (1280-50)/6

= 205 bacteria per day.

To find the rate of increase of colony, the most sitable method is to use the central derivative approximation formula.

The central derivative approximation says,

if `x_(n-1)` ,` x_n` and `x_(n+1)` are subsequent data of a data set and they are equally spaced by an interval of h,

`y'(x_n) = (y(x_(n+1)) - y(x_(n-1)))/(2h)`

This gives,

`r_2 = (357-153)/(2*1)`

`r_2 = 102 ` bacteria per day.

Therefore the rate of increase of colony at day 2 is 102 bacteria per day

Approved by eNotes Editorial Team