$f(x) = ab^x$

$a = y1$, $b = y2 / y1$ (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

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

Starts near zero and increases rapidly, approaching infinity as x increases.

Starts at a positive value and decreases rapidly, approaching zero as x increases.

It's the y-intercept of the graph (the value of y when x = 0).

Larger 'b' values (b > 1) result in steeper growth; smaller 'b' values (0 < b < 1) result in slower decay.

The limiting value that the function approaches as x goes to infinity.

It shifts the graph vertically by 'k' units.

The point where the two functions have the same value for the same input.

By observing how quickly the y-values increase for a given change in x.

An increasing exponential function that passes through (0, 1) and has a horizontal asymptote at y = 0 for x approaching negative infinity.

A decreasing exponential function that passes through (0, 1) and has a horizontal asymptote at y = 0 for x approaching positive infinity.

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.