Question

As the concert came to its end, the number of people in a stadium decreased every 10 minutes. The function p(x)=0.65(.96)x models the number of people in hundreds of thousands where x represents the number of 10-minute periods since the trend has been observed. What do the values in the function represent?

Answer 1

Answer: 0.65 represents the initial number of people in hundreds of thousands .

Also ,
`(0.96)=(1-0.04)`

It means the rate of decay = 0.04=4%

Explanation:

Given: The function
`p(x)=0.65(.96)^x` models the number of people in hundreds of thousands where x represents the number of 10-minute periods since the trend has been observed.

We know that the exponential decay function is given by :-

`f(x)=A(1-r)^x`, where A is the initial amount and r is the rate of decay in time x.

As compared to the given function we get

A = 0.65

It means the initial number of people = 0.65 hundreds of thousands =
`0.65*100*1000=65,000`

Also ,
`(0.96)=(1-0.04)`

Hence, the rate of decay = 0.04=4%

Answer 2

Answer: In the function,

`P(x) = 0.65 (0.96)^x`

0.65 represents the initial number of people in the concert.

0.96 is the negative growth factor per 10-minutes.

Explanation:

Since, Given function that shows the population after x minutes,

`P(x) = 0.65 (0.96)^x`

⇒
`P(x) = 0.65 (1-0.4)^x`

Thus, the number of people decrease by the rate 0.4.

since, initially, x = 0,

P(0) = 0.65

Thus, the initial number of people in the concert = 0.65 hundred = 65

Also, 0.96 is the negative growth factor of the function P(x).