a culture starts with 10000 and the number doubles every 40 mins.
a. find the function that models the number of bacteria at time t.
To find the function that models the number of bacteria at time t, we need to first understand the relationship between time and the number of bacteria.
In this case, we know that the number of bacteria starts with 10,000 and doubles every 40 minutes. This means that for every 40 minutes that pass, the number of bacteria is multiplied by 2.
Let's assume the function is represented by N(t), where N stands for the number of bacteria and t stands for time in minutes. We can write the initial condition as N(0) = 10,000.
Since the number of bacteria doubles every 40 minutes, we can write the growth factor as 2. Therefore, the function can be written as:
N(t) = N(0) * (2)^(t / 40)
where N(0) is the initial number of bacteria (10,000) and t is the time in minutes.
So, the function that models the number of bacteria at time t is N(t) = 10,000 * (2)^(t / 40).
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