A function of the form $f(x) = b + mx$, where $b$ is the y-intercept and $m$ is the slope.

The rate of change of a linear function; steepness and direction.

A sequence with a constant difference between consecutive terms, defined as $a_n = a_0 + dn$.

The constant value added to each term to get the next term.

A function of the form $f(x) = ab^x$, where $a$ is the initial value and $b$ is the base.

The factor by which the function's value changes for each unit increase in $x$.

A sequence with a constant ratio between consecutive terms, defined as $g_n = g_0 * r^n$.

The constant value by which each term is multiplied to get the next term.

The point where the line crosses the y-axis, where $x=0$.

The starting value of the function when x=0.

Linear: Constant rate of change (constant slope). Exponential: Proportional rate of change (constant ratio).

Arithmetic: Constant difference between terms. Geometric: Constant ratio between terms.

Linear: $f(x) = b + mx$ (addition). Exponential: $f(x) = ab^x$ (multiplication).

Linear: Constant addition of slope. Exponential: Constant multiplication by the base.

Linear: Initial value (y-intercept) and slope. Exponential: Initial value and base.

Sequences: Usually positive integers. Functions: Can have a wider range of values, like all real numbers.

Linear: Shifts and stretches affect slope and y-intercept directly. Exponential: Shifts and stretches affect initial value and base, impacting growth/decay rate.

Simple Interest: Modeled by linear functions (constant addition). Compound Interest: Modeled by exponential functions (constant multiplication).

Linear: Grows (or decays) at a constant rate. Exponential: Grows (or decays) much faster in the long run.

Linear: Look for constant addition/subtraction. Exponential: Look for constant multiplication/division (percentage increase/decrease).

1. Calculate the slope using $m = (y_2 - y_1) / (x_2 - x_1)$. 2. Use the point-slope form: $y - y_1 = m(x - x_1)$. 3. Simplify to slope-intercept form if needed.

Examine the base $b$ in $f(x) = ab^x$. If $b > 1$, it's growth. If 0 < b < 1, it's decay.

Substitute the number of years for $t$ in the function $V(t) = a(b)^t$ and calculate the result.

1. Substitute the points into $f(x) = ab^x$ to get two equations. 2. Solve for $a$ in one equation. 3. Substitute the expression for $a$ into the other equation and solve for $b$. 4. Substitute the value of $b$ back into the equation for $a$.

1. Set up the equation $V(t) = a(b)^t$. 2. Isolate the exponential term. 3. Take the logarithm of both sides. 4. Solve for $t$.

Subtract any term from its subsequent term: $d = a_{n+1} - a_n$.

Divide any term by its preceding term: $r = g_{n+1} / g_n$.

Use the identity $b^x = e^{x ln(b)}$, so $f(x) = ab^x$ becomes $f(x) = ae^{x ln(b)}$.

Use the point-slope form: $y - y_1 = m(x - x_1)$, where $(x_1, y_1)$ is the given point and $m$ is the slope. Then, rearrange to slope-intercept form if needed.

Find the y-value when x=0. This value is the initial value $a$ in the function $f(x) = ab^x$.