Compound Interest Formula: The amount $A$ in an account after $x$ years with principal $P$, compounded annually at rate $r$, is given by $A = P(1 + r)^x$.

Given Information:

• Principal (initial investment): $P = 100$
• Annual interest rate: $r = 5.5\% = 0.055$
• Compounding: once a year
• No deposits or withdrawals

Formula Derivation:

Using the compound interest formula:

$$A(x) = P(1 + r)^x$$

Substituting the values:

$$\boxed{A(x) = 100(1 + 0.055)^x = 100(1.055)^x}$$

where $x$ is the number of years elapsed since 2000, and $A(x)$ is the amount in dollars.

This is an exponential growth function with base $1.055$, meaning the investment grows by 5.5% each year.

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Even Function:

A function $f(x)$ is called even if $f(-x) = f(x)$ for all $x$ in its domain. Its graph is symmetric about the y-axis.

Odd Function:

A function $f(x)$ is called odd if $f(-x) = -f(x)$ for all $x$ in its domain. Its graph is symmetric about the origin.

Increasing Function:

A function $f(x)$ is increasing on an interval if for any $x_1 < x_2$ in that interval, $f(x_1) < f(x_2)$.

Decreasing Function:

A function $f(x)$ is decreasing on an interval if for any $x_1 < x_2$ in that interval, $f(x_1) > f(x_2)$.

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Analysis of $y = x^2$:

• For $x < 0$: as $x$ increases toward 0, $x^2$ decreases
  • Decreasing on $(-\infty, 0)$
• For $x > 0$: as $x$ increases from 0, $x^2$ increases
  • Increasing on $(0, \infty)$

Graph Description:

The graph of $y = x^2$ is a parabola opening upward with:

• Vertex at the origin $(0, 0)$
• Symmetric about the y-axis (since $x^2$ is an even function)
• Passes through points $(-2, 4)$, $(-1, 1)$, $(0, 0)$, $(1, 1)$, $(2, 4)$
• Decreases on the left side of y-axis and increases on the right side

Conclusion: The function $y = x^2$ is decreasing on $(-\infty, 0)$ and increasing on $(0, \infty)$, with a minimum value at $x = 0$.