We have been given that a community center holds an outdoor barbecue each year. In the first year, 96 people attended the event and the venue had a maximum capacity of 100 attendees. Each year since then, the event has grown in popularity by a factor of 30%. To accommodate the growing crowd, the venue increased its ability to accommodate people by 100 people each year.
Let t be number of years and A(t) be number of attendees after t years. We can see that attendance at the barbecue is increasing exponentially. Now we will use our given information to write an equation modeling the growth in attendance at the barbecue as:
[tex]A(t)=96\cdot(1.30)^{t}[/tex]
Therefore, [tex]A(t)=96\cdot(1.30)^{t}[/tex] will be our required model that represents the growth in attendance at the barbecue.
