Question

The sides of a square are 2 to the power of 4÷9 inches long. what is the area of the square?

Answer 1

side = 2^(4/9)
area = side^2 = ?

Answer 2

Wait what

Answer 3

How can I solve this??? @vocaloid

Answer 4

it gives you the length of one side, so to find the area, you just square the length

(side)*(side) = 2^(4/9) * 2^(4/9) = ?

Answer 5

Do I times it 4 times or just twice @vocaloid

Answer 6

twice..

Answer 7

@vocaloid

Answer 8

I got 4 to the power of 16/81

Answer 9

not quite, we have to use the exponent rule here

keep the base and add the exponents together

2^(4/9) * 2^(4/9) = 2^(4/9 + 4/9) = ?

Answer 10

Oh ok

Answer 11

Now I got 2 to the power of 8/9

Answer 12

Is that right? @vocaloid

Answer 13

yes, sorry for the late reply

Answer 14

Do you you think you can help me with another question? @vocaloid

Answer 15

sure

Answer 16

Given the function f(x) = 5^x , section A is from = x = 0 to x = 1 and the section B is from x = 2 to x = 3.

Part A: Find The average rate of change of each section

Part B: How many times greater is the average rate of change of section B then section A? Explain why one rate of change is greater than the other. @vocaloid

Answer 17

part A)

we want two values

1. the rate of change between x = 0 and x = 1
and
2. the rate of change between x = 2 and x = 3

so, let's just tackle the first part for now

the rate of change between x = 0 and x = 1 can be found using the formula

[f(1)-f(0)]/(1-0)

Answer 18

I got one

Answer 19

not quite, let's take it bit by bit

f(1) = ?

Answer 20

Is it one

Answer 21

not quite

f(x) = 5^x
f(1) = ?

Answer 22

5 to the power of one

Answer 23

right

now f(0) = ?

Answer 24

5 to the power of zero

Answer 25

right, so

[f(1)-f(0)]/(1-0) = ?

Answer 26

Is it 1/1

Answer 27

no...

remember, we just calculated f(1) and f(0)

f(1) - f(0) = ?

Answer 28

5^1 - 5^0

Answer 29

right, so

[f(1)-f(0)]/(1-0) = ?

Answer 30

Do I have to solve the exponent

Answer 31

yes

Answer 32

5-1/ 1-0 = 4/1

Answer 33

right, and 4/1 = ?

Answer 34

4

Answer 35

right, now let's calculate the rate of change from x = 2 to x = 3

[f(3)-f(2)]/(3-2) = ?

Answer 36

5^3 - 5^2/ 3-2

Answer 37

right, keep going...

Answer 38

125 - 25/ 3-2

Answer 39

right, keep going...

Answer 40

100/1= 100

Answer 41

right

Answer 42

now we're finished w/ part A

part B wants us to find (rate of change from x = 2 to x = 3)/(rate of change from x = 1 to x = 2)

using what we calculated earlier...

100/4 = ?

Answer 43

25

Answer 44

right so section B is 25 times as great (24 times greater) as section A

Answer 45

So that's the answer

Answer 46

as for "explain why" I would say something along the lines of
"f(x) is an increasing exponential function

Answer 47

yeah

Answer 48

Thank you