Let f (x) = 15/ 1+4e^-0.2x
What is the point of maximum growth rate for the
logistic function f(x)? Show all work.
Round your answer to the nearest hundredth.
Hint: Your answer should be an ordered pair.

  (6.931, 7.5)

Step-by-step explanation:

The point of maximum growth of a logistic function is always halfway between the horizontal asymptotes. Here, those are y=0 and y=15, so the point of interest is where f(x) = 15/2:

  15/2 = 15/(1+4e^(-.2x)) . . . . . use 15/2 for f(x)

  2 = 1 +4e^(-.2x) . . . . . . . . . . . match denominators

  1/4 = e^(-.2x) . . . . . . . . . . . . . subtract 1, divide by 4

  ln(1/4)/-0.2 = 5·ln(4) = x ≈ 6.93147 . . . . . . take natural logs, evaluate

The ordered pair (x, f(x)) is (6.93147, 7.5).

Answer: d. 39 cmin the diagram, the approximate length of the minor arc de is 39 centimetres.step-by-step explanation: the formula for the length of an arc in a circle is as displayed below.let the length of the minor arc de = xx = 2( pi )r × angle of sector / 360°from this, we will substitute the values given from the problem into the formula to obtain the length of the minor arc de.x = 2( pi )r × angle of sector / 360°r = radius = 25cmpi as an approximate value = 3.14angle of sector = 120°x = 2( 3.14 )( 25 ) × 120° / 360°x = 157 × 1 / 4x = 39.25x = 39 ( rounded to the nearest whole number as an approximate value )