Growth: b > 1, increases rapidly | Decay: 0 < b < 1, decreases rapidly.

Linear: Constant rate of change | Exponential: Constant proportional rate of change.

e: Models continuous growth/decay, related to natural logarithm | b: Models growth/decay over discrete intervals.

$e^x$: Exponential growth | $e^{-x}$: Exponential decay.

Exponential: Variable in exponent, rapid growth/decay | Polynomial: Variable in base, growth depends on degree.

Exponential: Unrestricted growth | Logistic: Growth limited by carrying capacity.

Positive: Increasing function | Negative: Decreasing function.

Different y-intercepts, but same growth/decay rate if 'b' is the same.

Exponential: Fits exponential model | Linear: Fits linear model. Use $R^2$ to determine best fit.

Inside: $f(x) = a b^{(x+c)}$: Horizontal shift | Outside: $f(x) = ab^x + c$: Vertical shift.

Growth increasing at an increasing rate; b > 1 in $f(x) = ab^x$.

Decay decreasing at a decreasing rate; 0 < b < 1 in $f(x) = ab^x$.

$f(x) = ab^x$, where 'a' is the initial value and 'b' is the base.

A mathematical constant approximately equal to 2.71828, used for continuous growth/decay.

A method to fit an exponential function to a set of data points.

A measure of how well the exponential model fits the data.

The difference between the observed data and the predicted values from the exponential model.

The natural logarithm, the inverse function of $e^x$.

A different representation of the same function that reveals different properties.

The value of the function when x = 0.

$f(x) = ab^x$

$a = y1$, $b = y2 / y1$ (when x1 = 0 and x2 = 1)

$f(x) = e^x$

$f(x) = e^{-x}$

$b = (y2/y1)^{1/(x2-x1)}$

$f(d) = (2^7)^{(d/7)}$

Growth factor = $b^{\Delta x}$, where $\Delta x$ is the length of the interval.

$P(t) = P_0 b^t$

$A(t) = A_0 b^t$, where 0 < b < 1

$e = \lim_{n \to \infty} (1 + \frac{1}{n})^n$