Question

In 2012, the number of people attending the South Coast Comic Convention was 5,000. The number of attendees continues to grow at a rate of 8.7% each year. If t is the number of years after 2012, write the equation in simplest form that could be used to determine how long it will take the number of attendees to reach 11,000.

Answer 1

Answer: $11000=5000(1.087)^t$

Explanation:

The exponential growth function is given by :-

$f(x)=A(1+r)^t$, where A is the initial value , r is rate of growth and t is the time period.

Given: The initial population of attendees (in 2012) =5,000

The rate of growth = 8.7 %=0.087

If t is the number of years after 2012 , then the exponential growth function that models the given situation will be :-

$f(x)=5000(1+0.087)^t\\\\\Righatrrow\ f(x)=5000(1.087)^t$

Now, the equation that could be used to determine how long it will take the number of attendees to reach 11,000 will be :-

$11000=5000(1.087)^t$

Answer 2

11000 = 5000(1.087)^t