Question

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.

Write an equation modeling the growth in attendance at the barbecue.

Answer 1

To model the growth in attendance at the barbecue each year, you can use the equation N = 96 * 1.3^(t-1) + 100*t, where N represents the number of attendees and t represents the number of years since the first year. This equation takes into account the initial attendance, the growth factor, and the increase in venue capacity each year.

Step-by-step explanation:

To model the growth in attendance at the barbecue, we can use an exponential equation. Let N represent the number of attendees each year and let t represent the number of years since the first year. The equation can be written as:

N = 96 * 1.3^(t-1) + 100*t

In this equation, 96 represents the initial attendance in the first year, 1.3 represents the growth factor (30% increase each year), and t-1 represents the number of years since the first year. The term 100*t represents the increase in venue capacity each year. By plugging in different values of t, you can find the attendance for each year.