Question

The table below shows the cube roots of different numbers:


Number
(x) 8 27 64 125
Cube root
(y) 2 3 4 5


Part A: Does the table represent y as a function of x? Justify your answer. (5 points)

Part B: The total cost f(x), in dollars, for renting a bike for x hours is shown below:

f(x) = 10 + 20x

What is the value of f(100), and what does f(100) represent? (5 points)

Answer 1

part A)

$\bf \begin{array}{|c|cccccc|ll} \cline{1-7} x&8&27&64&125&&x\\ \cline{1-7} y&\stackrel{\sqrt[3]{8}}{2}&\stackrel{\sqrt[3]{27}}{3}&\stackrel{\sqrt[3]{64}}{4}&\stackrel{\sqrt[3]{125}}{5}&&\sqrt[3]{x} \\ \cline{1-7} \end{array}~\hspace{10em}y = \sqrt[3]{x}$

part B)

f(x) = 10 + 20x

so if you rent the bike for a few hours that is

1 hr.............................10 + 20(1)

2 hrs..........................10 + 20(2)

3 hrs..........................10 + 20(3)

so the cost is really some fixed 10 + 20 bucks per hour, usually the 10 bucks is for some paperwork fee, so you go to the bike shop, and they'd say, ok is 10 bucks to set up a membership and 20 bucks per hour for using it, thereabouts.

f(100) = 10 + 20(100) => f(100) = 2010.

f(100), the cost of renting the bike for 100 hours.