Your friend sends out a chain letter email to 32 people. By the next day, 40 people have received the letter. Assuming an exponential growth pattern, by what percentage has the number of people receiving chain letters increased in this time frame?

(Express your answer as a percentage rounded to the nearest tenth.)

Sure! Let's solve this problem step-by-step.

1. Identify Initial and New Recipients:
- Initially, the chain letter was sent to 32 people.
- By the next day, 40 people have received the letter.

2. Calculate the Increase in People:
- Find out how many more people received the letter by subtracting the original number of recipients from the new number of recipients:
[tex]\[
\text{Increase} = 40 - 32 = 8
\][/tex]

3. Calculate the Percentage Increase:
- To find the percentage increase, divide the increase by the original number of people and multiply by 100:
[tex]\[
\text{Percentage Increase} = \left(\frac{8}{32}\right) \times 100
\][/tex]

4. Perform the Calculation:
- First, calculate [tex]$ \frac{8}{32} $[/tex] which equals 0.25.
- Then, multiply by 100 to convert it to a percentage:
[tex]\[
0.25 \times 100 = 25.0
\][/tex]

5. Rounding the Result:
- The percentage increase is 25.0%. This value is already rounded to the nearest tenth.

Therefore, the number of people receiving the chain letter increased by 25.0%.