Question

The number of visitors to a small pumpkin patch that opened in 2003 increased each year as shown in the table. Set up and solve an equation(s) to predict the number of visitors in 2020, assuming the increase continues at this same rate y=b(1+r)^t

Year 2003 2004 2005 2006 2007 2008
visitors 500 515 530 546 563 580

Answer 1

The equation is

`y=500(1+0.03)^t`, and the population in 2020 is 826.

We find the rate of increase using the formula
amount of change/original amount.

Using the first two data points, we have (515-500)/500 = 15/500 = 0.03. This is r.

b is the initial value, which in this case is 500.

This gives us the equation

`y=500(1+0.03)^t`

The first year, 2003, will be considered year 0, since it is before any changes took place. This means 2020 will be year (2020-2003) = 17:

`y=500(1+0.03)^(17) = 826.4\approx 826`