Exponential and Logarithmic Functions

Quadratic or polynomial trend data

Exponential growth or decay data

Cyclic or periodic function data

Linear relationship data

Maintains both steepness and linearity

Increases steepness and disrupts linearity

Decreases steepness while maintaining linearity

Increases steepness while maintaining linearity

Two units along t-axis.

Exactly one unit along t-axis.

Half-unit along t-axis.

Variable units depending on $P_0$.

Neither axis; it varies with each dataset represented on the plot.

The horizontal (x-axis)

Both axes equally often have logarithmic scales.

The vertical (y-axis)

Zero

Infinity

Negative but greater than negative one

Positive but less than one

It increases by an order of magnitude.

It decreases by an order of magnitude.

It remains constant.

It doubles.

Population variance information

Initial reproduction ratio

Maximum mortality

Carrying capacity

Neither axis is scaled logarithmically

The x-axis (horizontal)

The y-axis (vertical)

Both the x-axis and y-axis

As a rightward hyperbola moving toward infinity as time increases.

As an upward-opening parabolic curve with positive curvature throughout its domain.

As a straight line with positive slope.

As a downward-opening parabolic curve exhibiting negative curvature throughout its domain.

The variables have a quadratic relationship.

The variables have an exponential relationship.

The variables are not related.

The variables have a linear relationship.