An exponential function is a function that has the form y = ab^x, where a represents the initial value, and b represents the rate
(1) How to fill the table
The exponential function is given as:
[tex]y = 0.50(1.06)^x[/tex]
When x = 0, we have:
[tex]y = 0.50 * (1.06)^0 = 0.50[/tex]
When x = 10, we have:
[tex]y = 0.50 * (1.06)^{10} = 0.90[/tex]
When x = 20, 30 and 40 we have:
[tex]y = 0.50 * (1.06)^{20} = 1.60[/tex]
[tex]y = 0.50 * (1.06)^{30} = 2.87[/tex]
[tex]y = 0.50 * (1.06)^{40} = 5.14[/tex]
So, the complete table is:
Years after 1950 X : 0 | 10 | 20 | 30 | 40
Ticket Price $ Y : 0.50 | 0.90 | 1.60 | 2.87 | 5.14
(2) The y-intercept and the rate
The prices look reasonable.
The y-intercept is when x = 0.
So, the value of the y-intercept is 0.50
Also, the rate represents a growth.
This is so, because the rate is greater than 1
(3) The graph
See attachment for the graph of the exponential function
(4) The prices in 2000 and 2010
When x = 50 and 60, we have:
[tex]y = 0.50 * (1.06)^{50} = 9.21[/tex]
[tex]y = 0.50 * (1.06)^60} = 16.49[/tex]
Hence, the prices in 2000 and 2010 are $9.21 and $16.49
Read more about exponential functions at:
https://brainly.com/question/11464095
