Question

Function f(x)=5(2)ˣ represents the number of bacteria, f(x), growing in a culture after x hours. How many bacteria are in the culture after 3 hours?

Answer 1

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.