Question

Dominic sent a chain letter to his friends, asking them to forward the letter to more friends. The relationship between the elapsed time ttt, in hours, since Dominic sent the letter, and the number of people, P_{\text{hour}}(t)P hour ​ (t)P, start subscript, start text, h, o, u, r, end text, end subscript, left parenthesis, t, right parenthesis, who receive the email is modeled by the following function: Phour(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 .

Answer 1

The daily rate of change in the number of people who receive the email is a factor of approximately 3.58.

Step-by-step explanation:

The relationship between the elapsed time t, in hours, since Dominic sent the letter, and the number of people who receive the email is modeled by the function Phour(t) = 18 ⋅ (1.05)t. To find the daily rate of change, we need to calculate the factor by which the number of people grows every 24 hours. This can be done by plugging t = 24 (number of hours in a day) into the function.

Phour(24) = 18 ⋅ (1.05)24
Using a calculator, we find that Phour(24) ≈ 64.5. Therefore, the number of people grows by a factor of about 64.5/18 ≈ 3.58 every day. This means that every day, the number of people who receive the email grows by a factor of approximately 3.58. The daily rate of change in the number of people who receive the email can be determined by finding the factor by which the number of people grows each day. In this case, the function that models the relationship between time and the number of people is given by Phour(t) = 18 * (1.05)^t. To find the daily rate of change, we need to find the value of (1.05)^1, which represents the growth factor for one day.

(1.05)^1 = 1.05

Therefore, every day, the number of people who receive the email grows by a factor of 1.05.

Answer 2

Here's the answer. Have fun with it.