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Dominic sent a chain letter to his friends, asking them to forward the letter to more friends. The relationship between the elapsed time t, in hours, since Dominic sent the letter, and the number of people, P_("hour ")(t), who receive the email is modeled by the following function: P_("hour ")(t)=18*(1.05)^(t) Complete the following sentence about the daily rate of change in the number of people who receive the email. Round your answer to two decimal places. Every day, the number of people who receive the email grows by a factor of

Dominic sent a chain letter to his friends, asking them to forward the letter to more friends.\newlineThe relationship between the elapsed time t t , in hours, since Dominic sent the letter, and the number of people, Phour (t) P_{\text {hour }}(t) , who receive the email is modeled by the following function:\newlinePhour (t)=18⋅(1.05)t P_{\text {hour }}(t)=18 \cdot(1.05)^{t} \newlineComplete the following sentence about the daily rate of change in the number of people who receive the email.\newlineRound your answer to two decimal places.\newlineEvery day, the number of people who receive the email grows by a factor of

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Q. Dominic sent a chain letter to his friends, asking them to forward the letter to more friends.\newlineThe relationship between the elapsed time t t , in hours, since Dominic sent the letter, and the number of people, Phour (t) P_{\text {hour }}(t) , who receive the email is modeled by the following function:\newlinePhour (t)=18⋅(1.05)t P_{\text {hour }}(t)=18 \cdot(1.05)^{t} \newlineComplete the following sentence about the daily rate of change in the number of people who receive the email.\newlineRound your answer to two decimal places.\newlineEvery day, the number of people who receive the email grows by a factor of
  1. Convert to Days: To find the daily rate of change, we need to calculate the factor by which the number of people grows every day. Since the function is given in terms of hours, we need to convert the time to days. There are 2424 hours in a day, so we will substitute tt with 2424 to find the daily growth factor.
  2. Calculate Daily Growth Factor: Using the function Phour(t)=18×(1.05)tP_{\text{hour}}(t) = 18 \times (1.05)^t, we substitute tt with 2424 to find the daily growth factor.\newlinePday(24)=18×(1.05)24P_{\text{day}}(24) = 18 \times (1.05)^{24}
  3. Calculate (1.05)24(1.05)^{24}: Now we calculate the value of (1.05)24(1.05)^{24} using a calculator.(1.05)24≈2.663824(1.05)^{24} \approx 2.663824
  4. Round Daily Growth Factor: The daily growth factor is approximately 2.6638242.663824. This means that every day, the number of people who receive the email grows by a factor of about 2.6638242.663824. However, we need to round this to two decimal places as per the question prompt.
  5. Round Daily Growth Factor: The daily growth factor is approximately 2.6638242.663824. This means that every day, the number of people who receive the email grows by a factor of about 2.6638242.663824. However, we need to round this to two decimal places as per the question prompt.Rounding the daily growth factor to two decimal places gives us approximately 2.662.66.

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