Final answer:
To find the number of bacteria after 3 hours, we calculate f(3) = 5(2)^3, resulting in 40 bacteria. This demonstrates the principle of exponential growth in bacterial cultures.
Step-by-step explanation:
The number of bacteria in the culture after 3 hours can be calculated using the given function f(x)=5(2)x. To find the amount after 3 hours, we replace x with 3 and compute:
f(3) = 5(2)3
f(3) = 5(8)
f(3) = 40
Therefore, there will be 40 bacteria in the culture after 3 hours. This illustrates the concept of exponential growth, where the number of bacteria increases at a rapidly accelerating rate as each period passes, with the population doubling each hour in this specific scenario.