a) The continuous growth rate can be calculated using the formula:
r = (ln(B) - ln(A)) / t
where r is the continuous growth rate, A is the initial count (330), B is the count after 6 hours (1340), and t is the time elapsed (6 hours).
Substituting the values:
r = (ln(1340) - ln(330)) / 6
r = 0.3907
b) The model for the bacteria colony can be written as:
B = A * e^(rt)
where B is the number of bacteria after time t, A is the initial count (330), and e is the base of the natural logarithm.
c) To find the number of bacteria after 16 hours, substitute t = 16 and the values of A and r from above:
B = 330 * e^(0.3907 * 16)
B = 9581.57
The number of bacteria after 16 hours is approximately 9582.