Question

Ice bucket challenges for various causes have become quite common on social media. Participants challenge others to dump a bucket of ice water over their head or make a donation. The number of people participating in a challenge is an example of exponential growth and might be modeled by a function such as = 2(2.5)x . What does the 2.5 in this function represent?

Answer 1

• y=2(2.5)^x

As per general equation y=ab^x

• b is rate of change
• a is initial amount

Here 2 represents the no of people who started the test

• 2.5 is related to people participated

Option D is correct

Answer 2

Answer:

The average number of people each person challenged.

Step-by-step explanation:

Exponential Function

General form of an exponential function:

  $f(x)=ab^x$

where:

• a is the initial value (y-intercept)
• b is the base (growth/decay factor) in decimal form
  If b > 1 then it is an increasing function.
• If 0 < b < 1 then it is a decreasing function.
• x is the independent variable
• y is the dependent variable

Given exponential function:

$f(x)=2(2.5)^x$

Comparing the given function with the general function:

• a = 2
• b = 2.5
• y = number of people participating in the challenge

Therefore, 2 represents the initial value, i.e. the average number of people who started the challenge.

Therefore, 2.5 represents the growth factor, i.e. the average number of people each person challenged.

Learn more about exponential functions here:

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