Question

Given the function g(x) = 6x, Section A is from x = 1 to x = 2 and Section B is from x = 3 to x = 4.

Part A: Find the average rate of change of each section. (4 points)

Part B: How many times greater is the average rate of change of Section B than Section A? Explain why one rate of change is greater than the other. (6 points)

Answer 1

average rate of change means slope

for from x=1 to x=2, that is just the slope from (1,g(1)) to (2,g(2))

if you meant g(x)=6x, then the average rate of change for any section is going to be 6, answer for part A is 6 and part B is 0 times, and not applicable

if you meant g(x)=6ˣ, then that's more interesting, keep reading

A.

Section A

rate from x=1 to x=2

g(1)=6¹=6

g(2)=6²=36

slope from (1,6) to (2,36) is (36-6)/(2-1)=30/1=30

the average rate of change for section A is 30

section B

rate from x=3 to x=4

g(3)=6³=216

g(4)=6⁴=1296

slope from (3,216) to (4,1296) is (1296-216)/(4-3)=1080/1=1080

the average rate of change for section B is 1080

B.

hmm, 1080/30=36 times greater

it is greater because as an exponential function, the slope gets exponentially bigger, it doesn't increase by a set amount each time, it increases by a multipule of itself each time

Explanation:

Answer 2

average rate of change means slope
for from x=1 to x=2, that is just the slope from (1,g(1)) to (2,g(2))

if you meant g(x)=6x, then the average rate of change for any section is going to be 6, answer for part A is 6 and part B is 0 times, and not applicable

if you meant g(x)=6ˣ, then that's more interesting, keep reading

A.

Section A
rate from x=1 to x=2
g(1)=6¹=6
g(2)=6²=36
slope from (1,6) to (2,36) is (36-6)/(2-1)=30/1=30
the average rate of change for section A is 30

section B
rate from x=3 to x=4
g(3)=6³=216
g(4)=6⁴=1296
slope from (3,216) to (4,1296) is (1296-216)/(4-3)=1080/1=1080
the average rate of change for section B is 1080




B.
hmm, 1080/30=36 times greater
it is greater because as an exponential function, the slope gets exponentially bigger, it doesn't increase by a set amount each time, it increases by a multipule of itself each time