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Kylie sent a chain letter to her friends, asking them to forward the letter to more friends.

The relationship between the elapsed time [tex]\(t\)[/tex], in hours, since Kylie sent the letter, and the number of people, [tex]\(P(t)\)[/tex], who receive the email is modeled by the following function:
[tex]\[
P(t) = (1.09)^{6t + 25.5}
\][/tex]

Complete the following sentence about the hourly percent change in the number of people who receive the email. Round your answer to the nearest percent.

Every hour, there is a [tex]\(\square\)[/tex] [tex]\(\%\)[/tex] addition to/removal from the number of people who receive the email.



Answer :

GinnyAnswer
To determine the hourly percent change in the number of people receiving the email, we analyze the given exponential function:

[tex]\[ P(t) = (1.09)^{6t + 25.5} \][/tex]

Here's the step-by-step reasoning:

1. Identify the base of the exponential function: The base here is [tex]\(1.09\)[/tex].

2. Determine the percentage change per hour: The exponential growth rate is found by calculating the percentage change attributed to the base of the exponent. For an exponential function with the base [tex]\(b\)[/tex], the percentage change is given by [tex]\((b - 1) \times 100\)[/tex].

3. Calculate the hourly percentage increase: For our base [tex]\( 1.09 \)[/tex]:
[tex]\[ (1.09 - 1) \times 100 = 0.09 \times 100 = 9\% \][/tex]

4. Interpret the result: Since the base [tex]\(1.09\)[/tex] represents a growth factor, it is indicating an addition rather than a removal.

5. Conclusion: The statement should reflect that every hour, there is an addition to the number of people receiving the email.

So, completing the sentence:

"Every hour, there is a [tex]\(9\%\)[/tex] addition to the number of people who receive the email."