What is the y-intercept of the logistic function $$f(x) = \frac{30}{1 + 2e^{-0.5x}}$$ ?

The y-intercept is $$(0, 10)$$ .

What is the upper asymptote of the logistic function $$f(x) = \frac{60}{1 + 4e^{-2x}}$$ ?

The upper asymptote is $$y = 60$$ .

What is the lower asymptote of the logistic function $$f(x) = \frac{10}{1 + 3e^{-x}}$$ ?

The lower asymptote is $$y = 0$$ .

What is the significance of the parameter $$k$$ in a logistic function?

The parameter $$k$$ in a logistic function determines the steepness of the curve. A larger value of $$k$$ results in a steeper curve, indicating faster growth.

How does the value of $$x_0$$ affect the logistic function?

The value of $$x_0$$ in a logistic function determines the x-value at which the function's growth rate is the highest. It shifts the curve left or right.

What is the logistic growth model used for?

The logistic growth model is used to describe populations that grow rapidly at first and then slow down as they approach a carrying capacity, often seen in ecology and economics.

What is the formula for finding the value of a logistic function at a specific point?

The formula for finding the value of a logistic function at a specific point $$x$$ is: $$f(x) = \frac{L}{1 + e^{-k(x - x_0)}}$$ .

How do you find the value of $$f(0)$$ for the logistic function $$f(x) = \frac{15}{1 + 6e^{-x}}$$ ?

Substituting $$x = 0$$ gives $$f(0) = \frac{15}{1 + 6e^{0}} = \frac{15}{7} = 7.5$$ .

What is the lower asymptote of the logistic function $$f(x) = \frac{50}{1 + 7e^{-x}}$$ ?

The lower asymptote is $$y = 0$$ .

Honors PreCalc 3.1 Logistic functions

Flashcard

•

Mathematics

•

11th - 12th Grade

•

Practice Problem

•

Hard

•

CCSS

HSF-IF.C.7E, HSF.LE.B.5, HSF-IF.C.7D

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FLASHCARD QUESTION

Front

What is a logistic function?

Back

FLASHCARD QUESTION

Front

What is the general form of a logistic function?

Back

FLASHCARD QUESTION

Front

What does the upper asymptote of a logistic function represent?

Back

Tags

CCSS.HSF.LE.B.5

FLASHCARD QUESTION

Front

What does the lower asymptote of a logistic function represent?

Back

Tags

CCSS.HSF-IF.C.7E

FLASHCARD QUESTION

Front

How do you find the y-intercept of a logistic function?

Back

Tags

CCSS.HSF-IF.C.7E

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF-IF.C.7E

FLASHCARD QUESTION

Front

How do you determine the upper asymptote of a logistic function?

Back

Tags

CCSS.HSF-IF.C.7E

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