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

To determine the hourly percent change in the number of people who receive the email, let's analyze the given function: \[ P(t) = (1.09)^{6t + 25.5} \] This function can be rewritten to emphasize the hourly growth factor: \[ P(t) = (1.09^6)^t \times (1.09)^{25.5} \] Here, \( 1.09^6 \) represents the growth factor per hour. Let's calculate this: \[ 1.09^6 \approx 1.677 \] This means the number of people who receive the email multiplies by approximately 1.677 every hour. To find the percent increase: \[ \text{Percent Increase} = (1.677 - 1) \times 100\% \approx 67.7\% \] Rounding to the nearest percent, the hourly percent change is **68%**. **Completed Sentence:** Every hour, there is a **68 % increase** in the number of people who receive the email.