a) The continuous growth model for the bacteria is A = 25e^(0.39t), where A is the amount of bacteria after t hours.
The relative growth rate (r) of the bacteria can be found using the formula:
r = ln(1 + % rate of growth)
where ln is the natural logarithm.
We know that the continuous growth model is of the form A = P e^(rt), where P is the initial amount, r is the relative growth rate, and t is time. Comparing this to the given model, we can see that the initial amount is 25 and the relative growth rate is 0.39.
Substituting these values into the formula for the relative growth rate, we get:
0.39 = ln(1 + % rate of growth)
Solving for % rate of growth, we get:
% rate of growth = e^(0.39) - 1
% rate of growth = 0.4756
Therefore, the % rate of growth of the bacteria is approximately 47.56%.
b) To find the amount of bacteria after 3 hours, we can substitute t = 3 into the given model:
A = 25e^(0.39(3))
A = 25e^(1.17)
A ≈ 87.5
Therefore, there will be approximately 87.5 bacteria after 3 hours.