Question

The function f(x) = 4(2^x) represents the number of people who share a cat video x hours after it first appears on a website. How does the number of people sharing the video change each hour?

A. The number increases by 2 each hour.
B. The number doubles each hour.
C. The number increases by 4 each hour.
D. The number increases by a factor of 4 each hour.

Answer 1

The number of people sharing the cat video described by the function f(x) = 4(2^x) doubles each hour. This represents an exponential growth pattern where the base of the exponent indicates the factor by which the number increases.

Step-by-step explanation:

The function f(x) = 4(2^x) represents an example of exponential growth, where the amount increases by a constant factor over equal increments of time. In this particular case, the base of the exponent is 2, which means each hour the number of people sharing the video is multiplied by 2. Therefore, the number of people sharing the video doubles each hour. It is important to understand that exponential growth, such as this example, entails multiplying the previous amount by a constant base to get the amount at the next increment.

To put it into context, if we have 4 people sharing a video at the start (when x=0), one hour later (when x=1), there would be 4(2^1) = 8 people sharing it, and another hour later (when x=2), there would be 4(2^2) = 16 people sharing it, and so on. This pattern illustrates a doubling effect each hour.