So we have the exponential equation: [tex]y=18582(0.90)^x[/tex]
where
[tex]y[/tex] is the number of visitors
[tex]x[/tex] are the weekends since opening
1. Since the opening weekend is the day of the the park's opening, we just need to replace [tex]x[/tex] with [tex]0[/tex] in our exponential equation to get the number of visitors on the opening weekend:
[tex]y=18582(0.90)^x[/tex]
[tex]y=18582(0.90)^0[/tex]
[tex]y=18582(1)[/tex]
[tex]y=18582[/tex]
We can conclude that there were 18582 visitors on the opening weekend.
2. Just like before, to find the approximate number of visitors on the ninth weekend, we just need to replace [tex]x[/tex] with [tex]9[/tex] in our exponential equation:
[tex]y=18582(0.90)^x[/tex]
[tex]y=18582(0.90)^9[/tex]
[tex]y=7199.0475[/tex]
And rounded to the nearest integer:
[tex]y=7199[/tex]
We can conclude that there were approximately 7199 visitors on the [tex]9^{th}[/tex] weekend.
3. Here we know that the number of visitors is 15051. Since [tex]y[/tex] represents the number of visitors, we just need to replace [tex]y[/tex] with 15051 in our exponential equation and solve for [tex]x[/tex]:
[tex]y=18582(0.90)^x[/tex]
[tex]15051=18582(0.90)^x[/tex]
[tex] \frac{15051}{18582} =0.90^x[/tex]
[tex]0.90^x= \frac{5017}{6194} [/tex]
[tex]ln(0.90^x)=ln(\frac{5017}{6194})[/tex]
[tex]xln(0.90)=ln(\frac{5017}{6194})[/tex]
[tex]x= \frac{ln(\frac{5017}{6194})}{ln(0.90)} [/tex]
[tex]x=2.0002[/tex]
And rounded to the nearest whole number:
[tex]x=2[/tex]
We can conclude that the number of visitors was about 15,051 after 2 weekends.
