Understanding Logistic Functions

Why are logistic functions used instead of exponential growth functions in some scenarios?

• They are easier to calculate.

• They can model growth with limits.

• They are more visually appealing.

• They require fewer variables.

What condition must be met for a function to be considered a logistic growth function?

• The B value must be greater than 1.

• The B value must be less than 1.

• The K value must be negative.

• The C value must be zero.

What is the role of the C value in a logistic function?

• It determines the rate of growth.

• It is the limit to the growth.

• It is the decay rate.

• It is the initial value.

What is the lower horizontal asymptote for any logistic function?

• y = C

• y = 1

• y = 0

• y = B

What happens to the logistic function as x approaches negative infinity?

• It approaches infinity.

• It becomes undefined.

• It approaches the C value.

• It approaches zero.

What is the effect of a negative K value in a logistic function?

• It results in logistic decay.

• It results in logistic growth.

• It increases the C value.

• It has no effect.

In the first example, what is the y-intercept of the function f(x) = 8 / (1 + 3 * 0.7^x)?

• 1

• 2

• 3

• 4

What is the upper horizontal asymptote for the function f(x) = 8 / (1 + 3 * 0.7^x)?

• y = 8

• y = 3

• y = 0

• y = 1

In the second example, what is the y-intercept of the function G(x) = 20 / (1 + 2e^(-3x))?

• 8.33

• 7.67

• 5.33

• 6.67

What is the upper horizontal asymptote for the function G(x) = 20 / (1 + 2e^(-3x))?

• y = 5

• y = 0

• y = 20

• y = 10