The app below shows an example of [i][b]exponential growth[/b][/i]: you will learn how to create a simple mathematical model for a culture of bacteria. Explore it, using buttons and sliders.[br][br]([b]Note[/b]: The [i]doubling time[/i] of a population exhibiting exponential growth is the time required for a population to double, given that the population will always take the same amount of time to double.) [br][br]
A bacteria culture doubles in number every hour. The expression [math]112\cdot2^h[/math] gives the number of bacteria in the culture after [i]h[/i] hours.[br][br](a) What does the constant coefficient 112 mean?[br](b) What does the base 2 of the exponential term mean?[br](c) How many bacteria are there after 3 hours?
(a) 112 is the initial count of bacteria in the culture[br](b) 2 represents the doubling of the culture every hour[br](c) [math]112\cdot2^3=112\cdot8=896[/math] bacteria