Answer:
Step-by-step explanation:
The first question is asking you how many visitors there were, using the function model provided, when x = 0. Filling that in gives you:
[tex]y=18,582(.90)^0[/tex]
Anything to the 0 power = 1, so
y = 18,582(1) and
y = 18,582
The second question is asking you how many visitors there were on the 9th weekend, when x = 9:
[tex]y=18,582(.90)^9[/tex] and
[tex]y=18,582(.387420489)[/tex] so
y = 7199
The last question is asking on what weekend (unknown x) are there
y = 15.051 visitors. That requires using a log to solve for x. Set it up first:
[tex]15,051=18,582(.90)^x[/tex]
Start by dividing both sides by 18,582 to get:
[tex].8099773975=(.90)^x[/tex]
Now we need to take the log of both sides to get that x out from its exponential position. By taking the log of the right side, we are given the ability to bring the x down in front:
log(.8099773975) = x log(.90)
Now divide both sides by log(.90) to get
x = 2.000
That means that on the second weekend, there were approximately 15,051 visitors.
