Question
The operating costs, in dollars, for a business are increasing each week according to this function, where n equals the number of weeks of increase.
f
(
n
)
=
1500
(
1.005
)
n
Which statement best describes the meaning of
f
(
4
)
=
1530.2
?
A.
It gives the value for the number of weeks of increase.
B.
It means the operating costs equal $1,530.20 for week 4.
C.
It means the operating costs equal $1,530.20 for week 5.
D.
It gives the initial value for the cost of operation.
f
(
n
)
=
1500
(
1.005
)
n
Which statement best describes the meaning of
f
(
4
)
=
1530.2
?
A.
It gives the value for the number of weeks of increase.
B.
It means the operating costs equal $1,530.20 for week 4.
C.
It means the operating costs equal $1,530.20 for week 5.
D.
It gives the initial value for the cost of operation.
Answers
GPT-4o mini
To understand the expression \( f(4) = 1530.2 \), we can analyze the function \( f(n) = 1500(1.005)^n \). Here, \( n \) represents the number of weeks, and \( f(n) \) gives the operating costs after \( n \) weeks.
Specifically, \( f(4) = 1500(1.005)^4 \) calculates the operating costs at week 4. Therefore, \( f(4) = 1530.2 \) means that the operating costs for week 4 amount to $1,530.20.
Given that interpretation, the best statement that describes the meaning of \( f(4) = 1530.2 \) is:
**B. It means the operating costs equal $1,530.20 for week 4.**
Specifically, \( f(4) = 1500(1.005)^4 \) calculates the operating costs at week 4. Therefore, \( f(4) = 1530.2 \) means that the operating costs for week 4 amount to $1,530.20.
Given that interpretation, the best statement that describes the meaning of \( f(4) = 1530.2 \) is:
**B. It means the operating costs equal $1,530.20 for week 4.**