Finding the final amount in a word problem on continuous exponential.. The number of bacteria in a certain population is predicted to increase according to a continuous exponential growth model, at a relative rate of $16 \%$ per hour. Suppose that a sample culture has an initial population of 914 bacteria. Find the population predicted after five hours, according to the model. Do not round any intermediate computations, and round your answer to the nearest tenth. Dacteria

Step 1 ：The problem is asking for the population of bacteria after five hours given an initial population and a continuous growth rate. This is a classic problem of exponential growth, which can be modeled by the formula: \(P(t) = P0 * e^{rt}\) where: \(P(t)\) is the final amount after time t, \(P0\) is the initial amount, r is the growth rate, and t is the time.

Step 2 ：In this case, \(P0\) is 914, r is 16% or 0.16, and t is 5. We can plug these values into the formula to find the final population.

Step 3 ：Substituting the given values into the formula, we get: \(P(t) = 914 * e^{(0.16*5)}\)

Step 4 ：Solving the above expression, we get \(P(t) = 2034.1444086421156\)

Step 5 ：Rounding to the nearest tenth, we get \(P(t) = 2034.1\)

Step 6 ：Final Answer: The population predicted after five hours, according to the model, is approximately \(\boxed{2034.1}\)