The number y of hits a new search-engine website receives each month can be modeled by $y = 4080 e ^ { k t }$ 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) $k = 0.2988$ ;About 184,894,691,979 hits
B) $k = 0.2988$ ;About 2,921,047 hits
C) $k = 0.2988$ ;About 22,832,533,585 hits
D) $k = 0.2988$ ;About 57,970,933 hits
E) $k = 0.2988$ ;About 1,150,488,266 hits

Question

The number y of hits a new search-engine website receives each month can be modeled by $y = 4080 e ^ { k t }$ 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) $k = 0.2988$ ;About 184,894,691,979 hits
B) $k = 0.2988$ ;About 2,921,047 hits
C) $k = 0.2988$ ;About 22,832,533,585 hits
D) $k = 0.2988$ ;About 57,970,933 hits
E) $k = 0.2988$ ;About 1,150,488,266 hits

Quizplus · Accepted Answer

Given $y = 4080e^{kt}$ and $y = 10,000$ when $t = 3$, we solve for $k$ using $10,000 = 4080e^{3k}$. Dividing both sides by 4080 and taking the natural logarithm leads to $k = 0.2988$. To predict hits after 22 months, substitute $k = 0.2988$ and $t = 22$ into the original equation, yielding approximately 2,921,047 hits.

The Number Y of Hits a New Search-Engine Website Receives y=4080ekty = 4080 e ^ { k t }y=4080ekt

The Number Y of Hits a New Search-Engine Website Receives $y = 4080 e ^ { k t }$