Semi-log plot: One axis is logarithmic. | Log-log plot: Both axes are logarithmic.

Base-10: Easier to relate to orders of magnitude. | Base-e: Directly relates to exponential growth/decay constant.

Linear plot: Exponential data appears curved. | Semi-log plot: Exponential data appears linear.

Exponential growth: Positive slope. | Exponential decay: Negative slope.

Exponential data: Straight line on semi-log. | Polynomial data: Curve on semi-log.

Linear plot: Represents the initial value directly. | Semi-log plot: Represents the logarithm of the initial value.

Linear Plot: Represents the rate of change directly. | Semi-log plot: Represents the rate of exponential growth/decay.

Small range: Linear plot may be sufficient. | Large range: Semi-log plot is more effective at visualizing trends.

Logarithms: Linearize exponential relationships. | Other transformations: Used for different data distributions and relationships.

Growth: Slope is positive, indicating an increase over time. | Decay: Slope is negative, indicating a decrease over time.

$$\log_n(y) = \log_n(a) + x \log_n(b)$$\n$$y = (\log_n b)x + \log_n(a)$$

$$y = mx + b$$

$$m = \frac{\log(y_2) - \log(y_1)}{x_2 - x_1}$$

$$a = n^b$$, where n is the base of the logarithm.

$$y = 10^{mx+b}$$ (if base 10 logarithm)

$$y = ae^{kt}$$, where a is the initial value, k is the growth rate, and t is time.

$$y = ae^{-kt}$$, where a is the initial value, k is the decay rate, and t is time.

The slope and y-intercept of the linearized equation can be used to determine the parameters of the original exponential equation.

$$\log(ab) = \log(a) + \log(b)$$

$$\log(a^x) = x\log(a)$$

Indicates an exponential relationship between the x and y variables.

A faster rate of exponential growth or decay.

Indicates that the y-value is constant (no growth or decay).

Find the y-intercept of the linearized data and calculate its antilog.

Exponential growth.

Exponential decay.

Different bases will change the scale of the y-axis, affecting the slope's numerical value but not the overall trend.

The relationship is not purely exponential; it may be polynomial, logarithmic, or a combination of functions.

Compare the slopes of the lines representing each dataset. The steeper the slope, the faster the growth rate.

The data may have some error or noise, or the relationship may not be perfectly exponential.