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

- anonymous

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

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- Vocaloid

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

- anonymous

Wait what

- anonymous

How can I solve this??? @vocaloid

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- Vocaloid

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) = ?

- anonymous

Do I times it 4 times or just twice @vocaloid

- Vocaloid

twice..

- anonymous

@vocaloid

- anonymous

I got 4 to the power of 16/81

- Vocaloid

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) = ?

- anonymous

Oh ok

- anonymous

Now I got 2 to the power of 8/9

- anonymous

Is that right? @vocaloid

- Vocaloid

yes, sorry for the late reply

- anonymous

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

- Vocaloid

sure

- anonymous

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

- Vocaloid

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)

- anonymous

I got one

- Vocaloid

not quite, let's take it bit by bit
f(1) = ?

- anonymous

Is it one

- Vocaloid

not quite
f(x) = 5^x
f(1) = ?

- anonymous

5 to the power of one

- Vocaloid

right
now f(0) = ?

- anonymous

5 to the power of zero

- Vocaloid

right, so
[f(1)-f(0)]/(1-0) = ?

- anonymous

Is it 1/1

- Vocaloid

no...
remember, we just calculated f(1) and f(0)
f(1) - f(0) = ?

- anonymous

5^1 - 5^0

- Vocaloid

right, so
[f(1)-f(0)]/(1-0) = ?

- anonymous

Do I have to solve the exponent

- Vocaloid

yes

- anonymous

5-1/ 1-0 = 4/1

- Vocaloid

right, and 4/1 = ?

- anonymous

4

- Vocaloid

right, now let's calculate the rate of change from x = 2 to x = 3
[f(3)-f(2)]/(3-2) = ?

- anonymous

5^3 - 5^2/ 3-2

- Vocaloid

right, keep going...

- anonymous

125 - 25/ 3-2

- Vocaloid

right, keep going...

- anonymous

100/1= 100

- Vocaloid

right

- Vocaloid

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 = ?

- anonymous

25

- Vocaloid

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

- anonymous

So that's the answer

- Vocaloid

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

- Vocaloid

yeah

- anonymous

Thank you

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