Math help please

1. The ordered pairs (0, 1), (1, 4), (2, 16), (3, 64), and (4, 256) represent a function. What is a rule that represents this function?

y = 4^x
y = 4x
y = x^4
y = x + 4

2. Consider the relationship between the height of a tree and time. Time would be considered which of the following?

function
input function
independent variable
dependent variable

3. Which of the following describes the relationship between the length of a rectangle and its width as width varies and area stays the same?

As width decreases, length stays constant.
As width decreases, length increases.
As width decreases, length decreases.
As width increases, area increases.

My answers:
1. ?
2. independent variable
3. As width decreases, length increases.

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  1. well, zero out of three is not that great.

    1. did you notice
    4^0 = 1
    4^1 = 4
    4^2 = 16
    4^3 = 64 and
    4^4 = 256 ??

    2. The height of the tree in my backyard "depends" on how long it has been there, so ....

    3. suppose we have an area of 20 cm^2 and it stays at 20
    if the width = 2 cm, the length would be 10 cm
    if we increase the width to 4 cm, the length would be decreased to 5 cm.
    suppose we decrease the width from 4 to 3
    then the length will be 20/3 which is greater than 5

    you said that as width increases, the length increases, but I contradicted that with my example

    so what do you think?

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