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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?

Respuesta :

Answer:  In the function,

[tex]P(x) = 0.65 (0.96)^x[/tex]

0.65 represents the initial number of people in the concert.

0.96 is the negative growth factor per 10-minutes.

Step-by-step explanation:

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

[tex]P(x) = 0.65 (0.96)^x[/tex]

⇒ [tex]P(x) = 0.65 (1-0.4)^x[/tex]

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).


JeanaShupp

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

Also , [tex](0.96)=(1-0.04)[/tex]

It means the rate of decay = 0.04=4%

Step-by-step explanation:

Given: The function [tex]p(x)=0.65(.96)^x[/tex] 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 :-

[tex]f(x)=A(1-r)^x[/tex], 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 =[tex]0.65\times100\times1000=65,000[/tex]

Also , [tex](0.96)=(1-0.04)[/tex]

Hence, the rate of decay = 0.04=4%

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