Question

A singer's newly announced concert on social media received 600 mentions in the first week of its announcement. The total number of mentions increases by half every week. Based on this information, after how many weeks since the concert was announced will the total number of mentions increase to about 4,556?

Answer 1

Answer: D. The total number of mentions will increase about 4,566 after 5 weeks.

Explanation:

Given: In the first week, the number of mentions received by social media = 600

Since, the total number of mentions increases by half every week.

Therefore, they will increase exponentially with the rate of increase = 50%=0.5

let x be the number of weeks since the concert was announced will the total number of mentions increase to about 4,556.

Then, according to the question, we have

`600(1+0.5)^x=4556\\\Rightarrow\ (1.5)^x=(4556)/(600)\\\Rightarrow\ (1.5)^x=7.59\\\text{Taking log on both the sides , we get}\\\\\Rightarrpw\ x\log(1.5)=log(7.59)\\\Rightarrow\ x(0.1760)=0.88\\\Rightarrow\ x=(0.88)/(0.176)\\\Rightarrow\ x=5`

Hence, The total number of mentions will increase about 4,566 after 5 weeks.