The number of bacteria in a certain culture increases from 600 to 1800 between 6:00am and 8:00am. a) Assuming that the growth rate of the number of bacteria is proportional to the number of bacteria present, we can write dn = kn, where the number of bacteria n is a function of time t. By integration and using the given information, find the value of k. b) Using the value of k found in item a), i. write the exponential growth equation for n(t); ii. then, simplify your answer to the form n(t) = Cabt, where a is an integer, C and b are constants to be determined, and n(t) is the number of bacteria as a function of time t. c) What is the number of bacteria present at 10:00am? d) At what time, in hours and minutes, will there be 9000 bacteria present in the culture?

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