Question

Five students received the same text message at 9:00 AM

Each of them sent the message to 5 more students at
10:00 AM. Each of those students sent the message to
5 more students at 11:00 AM.

Answer 1

a) 625

b) 2:00 PM

Explanation:

Note: The complete question is in the image attached with.

Part a)

Number of students who received text message at 9:00 AM = 5 =
`5^(1)`

Since each of them sent the text to 5 more students, number of students who received text by 10 AM = 5 x 5 = 5² =
`5^(1+1)`

Each of these students sent the message to 5 more students, so number of students who received text at 11 AM = 5 x 5 x 5 = 5³ =
`5^(1+2)`

If this pattern continues, we can represent it using the following exponential expression:

`N=5^(1+x)`

Here, x is the number of hours after 9:00 AM and N represents the number of students who received the text after x hours. We have to find how many students would have received text by noon i.e. at 12 PM which is 3 hours after 9 AM. So, if we replace x by 3, we will get the number of students who received the text at noon.

`N=5^(1+3)=5^(4)=625`

Thus, 625 students would have received texts by noon.

Part b)

For this part we need to find the time when 15625 students would have received the texts. We have the value of N, we need to find the value of x. Using the value in the above formula, we get:

`15625=5^(1+x)\\5^(6)=5^(1+x)`

Since, the basis are same, the exponents must be equal. So,

6 = 1 + x

x = 5

This means, 5 hours after 9 AM, 15625 students would have received the text. 5 hours after 9 AM means 2 PM. So, by 2 PM, 15625 students would have received the texts.