Answer: D. The total number of mentions will increase about 4,566 after 5 weeks.
Step-by-step 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
[tex]600(1+0.5)^x=4556\\\Rightarrow\ (1.5)^x=\frac{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=\frac{0.88}{0.176}\\\Rightarrow\ x=5[/tex]
Hence, The total number of mentions will increase about 4,566 after 5 weeks.
