What is the value of c in the logistic function y = 75 1 + 24 e − 0.125 x y=\frac{75}{1+24e^{-0.125x}} y = 1 + 2 4 e − 0 . 1 2 5 x 7 5 ?

c = 0.125 c=0.125 c = 0 . 1 2 5

Find the y-intercept of f ( x ) = 8 1 + 5 e − 1 2 x f\left(x\right)=\frac{8}{1+5e^{-\frac{1}{2}x}} f ( x ) = 1 + 5 e − 2 1 x 8

( 0 , 1. 3 ‾ ) \left(0,\ 1.\overline{3}\right) ( 0 , 1 . 3 )

( 0 , 2 ) \left(0,\ 2\right) ( 0 , 2 )

( 0 , 13 ) \left(0,\ 13\right) ( 0 , 1 3 )

( 0 , 4 ) \left(0,\ 4\right) ( 0 , 4 )

Which of the following gives the correct y-intercept for any logistic function f ( x ) = c 1 + a e − b x f\left(x\right)=\frac{c}{1+ae^{-bx}} f ( x ) = 1 + a e − b x c ?

( 0 , c 1 + a ) \left(0,\ \frac{c}{1+a}\right) ( 0 , 1 + a c )

( 0 , c 1 + a e ) \left(0,\ \frac{c}{1+ae}\right) ( 0 , 1 + a e c )

( 0 , c 1 − a ) \left(0,\ \frac{c}{1-a}\right) ( 0 , 1 − a c )

( 0 , c ) \left(0,\ c\right) ( 0 , c )

Find the point where the rate of growth is at its highest in the function y = 16 1 + 4 e − 0.24 x y=\frac{16}{1+4e^{-0.24x}} y = 1 + 4 e − 0 . 2 4 x 1 6 .

( 5.8 , 8 ) \left(5.8,\ 8\right) ( 5 . 8 , 8 )

( 16.6 , 8 ) \left(16.6,\ 8\right) ( 1 6 . 6 , 8 )

( 0 , 8 ) \left(0,\ 8\right) ( 0 , 8 )

( 4.2 , 8 ) \left(4.2,\ 8\right) ( 4 . 2 , 8 )

We know that the y-value of the point of maximum growth is half of the upper asymptote ( c 2 ) \left(\frac{c}{2}\right) ( 2 c ) . So, for any logistic function f ( x ) = c 1 + a e − b x f\left(x\right)=\frac{c}{1+ae^{-bx}} f ( x ) = 1 + a e − b x c , find the exact x -value of the point of maximum growth.

ln ⁡ a b \frac{\ln a}{b} b ln a

ln ⁡ ( a b ) \ln\left(\frac{\sqrt{a}}{b}\right) ln ( b a <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> )

b ln ⁡ ( a ) b\ln\left(a\right) b ln ( a )

ln ⁡ ( b a ) \ln\left(^b\sqrt{a}\right) ln ( b a <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> )

Graph Analysis of Logistic Functions (MA 4.21/22.2022)

Authored by Karen Lorenz

Mathematics

10th Grade - University

CCSS covered

Used 12+ times

Graph Analysis of Logistic Functions (MA 4.21/22.2022)

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MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Which of the following functions is logistic?

$f\left(x\right)=-2\log_ex$

$f\left(x\right)=\ln\left(x+2\right)$

$f\left(x\right)=\frac{1}{1+e^{-0.1x}}$

$f\left(x\right)=4e^{\left(x-1\right)}$

Tags

CCSS.HSF.LE.A.2

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

CCSS.HSF.LE.A.1

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Which of the following logistic functions has an a-value equal to 4?

$g\left(x\right)=\frac{32}{1+3e^{-4x}}$

$g\left(x\right)=\frac{4}{1+2e^{-0.5x}}$

$g\left(x\right)\ =\frac{79}{1+4e^{-0.125x}}$

$g\left(x\right)=\frac{8}{1+8e^{4x}}$

Tags

CCSS.HSF.LE.A.2

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Find the upper asymptote for the logistic function $f\left(x\right)=\frac{60}{1+4e^{-2x}}$ .

$y=60$

$y=120$

$y=15$

$y=12$

Tags

CCSS.HSF-IF.C.7E

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Which of the following logistic functions has an asymptote at y = 8?

$y=\frac{8}{1+2e^{-0.5x}}$

$y=2e^{-0.5x}+8$

$y=\ln\left(x-8\right)$

$y=\frac{8}{1-e^x}$

Tags

CCSS.HSF-IF.C.7E

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

What is the value of a in the logistic function $y=\frac{6}{1+3e^{-2x}}$ ?

$a=1$

$a=2$

$a=3$

$a=6$

Tags

CCSS.HSF.LE.A.2

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

What is the value of c in the logistic function $y=\frac{75}{1+24e^{-0.125x}}$ ?

$c=24$

$c=0.125$

$c=25$

$c=75$

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Find the value of c in the equation of the graphed logistic function:

$c=2$

$c=4$

$c=3$

$c=1$

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

CCSS.HSF.LE.A.1

CCSS.HSA.REI.D.11

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Find the y-intercept of $f\left(x\right)=\frac{8}{1+5e^{-\frac{1}{2}x}}$

$\left(0,\ 1.\overline{3}\right)$

$\left(0,\ 2\right)$

$\left(0,\ 13\right)$

$\left(0,\ 4\right)$

Tags

CCSS.HSF-IF.C.7E

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Which of the following gives the correct y-intercept for any logistic function $f\left(x\right)=\frac{c}{1+ae^{-bx}}$ ?

$\left(0,\ \frac{c}{1+ae}\right)$

$\left(0,\ \frac{c}{1-a}\right)$

$\left(0,\ c\right)$

$\left(0,\ \frac{c}{1+a}\right)$

Tags

CCSS.HSF-IF.C.7E

10.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Find the point where the rate of growth is at its highest in the function $y=\frac{16}{1+4e^{-0.24x}}$ .

$\left(5.8,\ 8\right)$

$\left(16.6,\ 8\right)$

$\left(0,\ 8\right)$

$\left(4.2,\ 8\right)$

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Graph Analysis of Logistic Functions (MA 4.21/22.2022)

Which of the following functions is logistic?

Which of the following logistic functions has an a-value equal to 4?

Find the upper asymptote for the logistic function f(x)=601+4e−2xf\left(x\right)=\frac{60}{1+4e^{-2x}}f(x)=1+4e−2x60​ .

Which of the following logistic functions has an asymptote at y = 8?

What is the value of a in the logistic function y=61+3e−2xy=\frac{6}{1+3e^{-2x}}y=1+3e−2x6​ ?

What is the value of c in the logistic function y=751+24e−0.125xy=\frac{75}{1+24e^{-0.125x}}y=1+24e−0.125x75​ ?

Find the value of c in the equation of the graphed logistic function:

Find the y-intercept of f(x)=81+5e−12xf\left(x\right)=\frac{8}{1+5e^{-\frac{1}{2}x}}f(x)=1+5e−21​x8​

Which of the following gives the correct y-intercept for any logistic function f(x)=c1+ae−bxf\left(x\right)=\frac{c}{1+ae^{-bx}}f(x)=1+ae−bxc​ ?

Find the point where the rate of growth is at its highest in the function y=161+4e−0.24xy=\frac{16}{1+4e^{-0.24x}}y=1+4e−0.24x16​ .

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Discover more resources for Mathematics

Find the upper asymptote for the logistic function $f\left(x\right)=\frac{60}{1+4e^{-2x}}$ .

What is the value of a in the logistic function $y=\frac{6}{1+3e^{-2x}}$ ?

What is the value of c in the logistic function $y=\frac{75}{1+24e^{-0.125x}}$ ?

Find the y-intercept of $f\left(x\right)=\frac{8}{1+5e^{-\frac{1}{2}x}}$

Which of the following gives the correct y-intercept for any logistic function $f\left(x\right)=\frac{c}{1+ae^{-bx}}$ ?

Find the point where the rate of growth is at its highest in the function $y=\frac{16}{1+4e^{-0.24x}}$ .