Question

question 12 of 25
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 a factor of 4 each hour.

b. the number increases by 4 each hour.

c. the number increases by 2 each hour.

d. the number doubles each hour.

Explanation:

Step1: Recall exponential function form

The general form of an exponential function is \( f(x) = a(b)^x \), where \( a \) is the initial amount and \( b \) is the growth factor (if \( b>1 \)) or decay factor (if \( 0 < b < 1 \)).

Step2: Identify components of given function

For the function \( f(x)=4(2)^x \), we have \( a = 4 \) (initial number of people sharing the video) and \( b = 2 \).

Step3: Analyze the growth factor

The growth factor \( b = 2 \) means that for each increase of 1 in \( x \) (each hour), the function value is multiplied by 2. In other words, the number of people sharing the video doubles each hour.
Let's check with \( x = 0 \): \( f(0)=4(2)^0 = 4(1)=4 \).
For \( x = 1 \): \( f(1)=4(2)^1 = 8 \), which is double of 4.
For \( x = 2 \): \( f(2)=4(2)^2 = 16 \), which is double of 8.
This confirms that the number doubles each hour.

Answer:

D. The number doubles each hour.