Question

Let f(x)=18/1+3^e-0.1x What is the point of maximum growth rate for the logistic function f(x)? Show all work. Round your answer to the nearest hundredth

Answer 1

(0, 4.5)

Step-by-step explanation:

*The equation can be put into Desmos, to find the point, but the work to prove it is here*

f(x)=c/1+Ae^-Bx

Y=C

C=18 A=3 -B=-0.1

*Replace x with 0 in the equation, so you know 0 is the x value, and it leads you to the y value*

f(0)=18/1+3e^-o.1(0)

= 18/1+3e^0

=18/1+3(1)

=18/1+3

=18/4

=4.5

x=0 y=4.5

Maximum growth rate = (x,y) --> (0, 4.5)

Hope this helps:))!!