Question

example 6

1. geometry the volume for any cube is given by the function (f(x)=x^{3}), where (x) is the length of a side of the cube. find and interpret (f(4)).
2. parking a parking garage charges (8 for the first two hours and (1.75 for each additional hour. the function for the cost of parking in the garage for (x) hours is (f(x)=8 + 1.75(x - 2)), where (x) is the number of total hours. find and interpret (f(7)).

Explanation:

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Step1: Recall volume formula for cube

The volume formula for a cube is $V = x^{3}$, where $x$ is the side - length of the cube.

Step2: Find $f(4)$

Substitute $x = 4$ into the function $f(x)=x^{3}$. So $f(4)=4^{3}=4\times4\times4 = 64$.

Step3: Interpret $f(4)$

The value $f(4) = 64$ means that the volume of a cube with side - length $x = 4$ is 64 cubic units.

Step1: Find $f(7)$

Given the function $f(x)=8 + 1.75(x - 2)$ for $x\geq2$. Substitute $x = 7$ into the function.
First, calculate the value inside the parentheses: $x-2=7 - 2=5$.
Then, multiply by 1.75: $1.75\times5 = 8.75$.
Finally, add 8: $f(7)=8+8.75=16.75$.

Step2: Interpret $f(7)$

The value $f(7)=16.75$ means that the cost of parking for 7 hours in the parking garage is $16.75.

Answer:

$f(4)=64$. The volume of a cube with side - length 4 is 64 cubic units.

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