Question

The table of values represents a logistic function ​f(x)​.

How much greater is the average rate of change over the interval [1,3] than the interval [−4,−2] ?

Answer 1

here's the image

Answer 2

this formula looks a little intimidating but I'll break it down for you

Answer 3

this is the average rate of change from x = a to x = b (a and b just represent generic values, we can substitute the values from our problem into this formula)

Answer 4

so, "average rate of change" over [1,3] means a = 1 and b = 3, giving us...

Answer 5

now, first we find f(3) - f(1)

f(3) just means "the value of the function at x = 3"

so if we look at the table, what does the function equal when x = 3?

Answer 6

2?

Answer 7

ohh right right i was looking at the equation

Answer 8

15.882

Answer 9

good, what about f(1) = ?

Answer 10

11.38

Answer 11

good, so f(3) - f(1) = 15.882 - 11.38 = 4.502

Answer 12

now, 4.502 divided by (3-1) is just 4.502/2 = 2.251 which is the rate of change for [1,3]

now we just repeat the whole thing for [−4,−2]

Answer 13

f(-2) = ?

Answer 14

sorry my browser closed suddenly

Answer 15

15.167

Answer 16

that's positive 2 ^^ we're looking for f(-2)

Answer 17

oops sorry that was 0.0971 and then minus function of -4

Answer 18

0.0018

Answer 19

good, so:

f(-2) - f(-4) = 0.0971 - 0.0018 = 0.0953

then divide that by (-2 - (-4)) which is just 2

so rate of change = 0.0953/2 = 0.04765

Answer 20

final step: the question asks "how much greater" so

2.251 - 0.04765 = 2.20335 = your answer

Answer 21

awesome thanks again for your help :) @Vocaloid