The table of values is an illustration of an exponential function
The equation for the projected number of visitors after n years is [tex]a_n = 4 * 1.5^{n - 1}[/tex]
How to determine the equation
An exponential function is represented as:
[tex]y = ab^x[/tex]
From the table, we have:
(x,y) = (1,4) and (2,6)
So, we have:
[tex]y = ab^x[/tex]
[tex]ab^1 = 4[/tex]
[tex]ab =4[/tex]
Also, we have:
[tex]ab^2 = 6[/tex]
Divide both equations
[tex]ab^2 \div ab = 6 \div 4[/tex]
[tex]b = 1.5[/tex]
Substitute 1.5 for b in ab = 4
So, we have:
[tex]1.5a = 4[/tex]
Divide through by 1.5
[tex]a = \frac{4}{1.5}[/tex]
Recall that:
[tex]y = ab^x[/tex]
So, we have:
[tex]y = \frac 4{1.5} * 1.5^x[/tex]
This gives
[tex]y = 4 * 1.5^{x - 1}[/tex]
Rewrite as:
[tex]a_n = 4 * 1.5^{n - 1}[/tex]
Hence, the equation for the projected number of visitors after n years is [tex]a_n = 4 * 1.5^{n - 1}[/tex]
Read more about exponential functions at:
https://brainly.com/question/11464095
