Answer:
1) There were 18582 visitors on the opening weekend.
2) There were approximately 7199 visitors on the 9th weekend.
3) The number of visitors was about 15,051 after 2 weekends.
Step-by-step explanation:
Given : The curve of best fit to model the data is given below.
[tex]y=18582(0.90)^x[/tex]
To find : Complete the statements,
1) There were _____ visitors on the opening weekend.
2) There were approximately _____ visitors on the 9th weekend.
3) The number of visitors was about 15,051 after ______ weekends.
Solution :
[tex]y=18582(0.90)^x[/tex] is the exponential equation:
where, y is the number of visitors and x are the weekends since opening
1. Since the opening weekend is the day of the the park's opening.
So, replace x=0 in our exponential equation to get the number of visitors on the opening weekend:
[tex]y=18582(0.90)^x\\y=18582(0.90)^0\\y=18582(1)\\y=18582[/tex]
Therefore, There were 18582 visitors on the opening weekend.
2. To find the approximate number of visitors on the ninth weekend.
We replace x=9 in our exponential equation:
[tex]y=18582(0.90)^x\\y=18582(0.90)^9\\y=7199.0475[/tex]
Rounded to the nearest integer : y=7199
Therefore, There were approximately 7199 visitors on the 9th weekend.
3. Here, we know that the number of visitors is 15051
Since y represents the number of visitors.
So, replace y=15051 in our exponential equation and solve for x:
[tex]y=18582(0.90)^x\\\\15051=18582(0.90)^x\\\\ \frac{15051}{18582} =0.90^x\\\\0.90^x= \frac{5017}{6194} \\\\ln(0.90^x)=ln(\frac{5017}{6194})\\\\xln(0.90)=ln(\frac{5017}{6194})\\\\x= \frac{ln(\frac{5017}{6194})}{ln(0.90)} \\\\x=2.0002[/tex]
Rounded to the nearest whole number : x=2
Therefore, The number of visitors was about 15,051 after 2 weekends.
