A bacteria culture contains 1400 bacteria initially and doubles every hour.(a) Find a function N that models the number of bacteria after t hours.N(t) = (b) Find the number of bacteria after 24 hours. bacteria
Question
A bacteria culture contains 1400 bacteria initially and doubles every hour.(a) Find a function N that models the number of bacteria after t hours.N(t) = (b) Find the number of bacteria after 24 hours. bacteria
Solution
(a) The function N that models the number of bacteria after t hours is an exponential growth function. Since the bacteria doubles every hour, the function is:
N(t) = 1400 * 2^t
where:
- N(t) is the number of bacteria after t hours,
- 1400 is the initial number of bacteria, and
- t is the time in hours.
(b) To find the number of bacteria after 24 hours, substitute t = 24 into the function:
N(24) = 1400 * 2^24
Calculate 2^24 and then multiply the result by 1400 to get the number of bacteria after 24 hours.
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