Answer:
The initial amount
Step-by-step explanation:
Given

See comment for complete question
Required
What 5000 represents
The given formula represents an exponential function

Where
initial value
So, by comparison:

<em>In this context, 5000 represents the initial amount</em>
Answer:

Step-by-step explanation:
Assuming We want to evaluate

When y=6 and z=3.
We substitute to get:

We multiply to get:

We simplify the denominator to get:

Reduce the first fraction:

Add the numerator and keep one denominator for they are like fractions

Write as a mixed number:

Answer:
a. 80 students
b. 92 students
Step-by-step explanation:
Represent arts students with A and Dance students with D.
So, we have,
n(A) = 35
n(D) = 57
Required
Determine n(A or D)
Solving (a):
Here, we have:
n(A and D) = 12
n(A or D) is calculated as thus:
n(A or D) = n(A) + n(D) - n(A and D)
n(A or D) = 35 + 57 - 12
n(A or D) = 80
b. From the given details
n(A and D) = 0 because both students are not mixed up as in (a) above
Using the same formula as (a).
n(A or D) = n(A) + n(D) - n(A and D)
n(A or D) = 35 + 57 - 0
n(A or D) = 92