The number y of hits a new search-engine website receives each month can be modeled by where t represents the number of months the website has been operating.In the website's third month, there were 10,000 hits.Find the value of k, and use this value to predict the number of hits the website will receive after 22 months.
A) ; About 184,894,691,979 hits
B) ; About 2,921,047 hits
C) ; About 22,832,533,585 hits
D) ; About 57,970,933 hits
E) ; About 1,150,488,266 hits

Question

The number y of hits a new search-engine website receives each month can be modeled by  where t represents the number of months the website has been operating.In the website's third month, there were 10,000 hits.Find the value of k, and use this value to predict the number of hits the website will receive after 22 months. ​
A) ; About 184,894,691,979 hits 
B) ; About 2,921,047 hits 
C) ; About 22,832,533,585 hits 
D) ; About 57,970,933 hits 
E) ; About 1,150,488,266 hits

Quizplus · Accepted Answer

First, we are given that the equation for the website's hits is:

y = 11e^(kt)

We are also given that in the third month, y = 10,000. Plugging this into the equation gives:

10,000 = 11e^(3k)

Solving for k:

k = ln(10,000/11)/3

k ≈ 0.049

Now that we have found k, we can use it to predict the number of hits after 22 months:

y = 11e^(0.049*22) ≈ 2,921,047

Therefore, the best choice is B.

The Number Y of Hits a New Search-Engine Website Receives