The function f(t)=3e^t represents the population of a strand of bacteria, where t is time in hours. What is the population after 30 minutes?
well, that would be
3e^(30/60), right?
To find the population after 30 minutes, we need to convert the time from minutes to hours, since the function is given in terms of hours.
There are 60 minutes in an hour, so 30 minutes is equivalent to 30/60 = 0.5 hours.
Now, we can plug this value into the function f(t) = 3e^t to find the population after 30 minutes:
f(0.5) = 3e^(0.5)
To evaluate this, we need to know the approximate value of e, which is a mathematical constant approximately equal to 2.71828.
Calculating the population using a calculator or software:
f(0.5) = 3 * e^(0.5) ≈ 3 * 1.648721 = 4.946163
So, the population after 30 minutes is approximately 4.946163 bacteria.