Question

help!!!! The function fx=(1.006235)^12x models the monthly interest that a bank offers to dan after x years. Dan converts the function to have x isolated in the exponent. What is the approximate rate of growth?

Answer 1

@Loser66

Answer 2

@zepdrix

Answer 3

\[\Large\rm f(x)=(1.006235)^{12x}\]
An important rule of exponents to remember:\[\Large\rm \color{royalblue}{a^{bc}=(a^b)^c}\]

Answer 4

Applying the rule allows us to isolate our x:
\[\Large\rm f(x)=\left(1.006235^{12}\right)^x\]

Answer 5

so I can do 1.006235^12 ?

Answer 6

Yah, what does that give you? :)

Answer 7

1.077439845599 so 1%?

Answer 8

the 1. represents 100%.
You can split it up like this if it will help to see what's going on.\[\Large\rm (1.0774)^x=(1 +\color{orangered}{.0774})^x\]The 1 represents the previous whole amount.
The orange part is the rate of grown portion.

Answer 9

so its A?

Answer 10

So what is that value, that decimal, written as a percent?\[\Large\rm .0774 =\text{_%}\]

Answer 11

No, it is not A.

Answer 12

7.74

Answer 13

WHICH 8%

Answer 14

Approximately 8%?

Yayyy good job \c:/

Answer 15

THAT MAKES SENSE!! LOL THANKS :)

Answer 16

CAN YOU HELP ME ON SIMPLIFYING?

Answer 17

@zepdrix

Answer 18

CAN YOU HELP ME WITH #6? I TOTALLY FORGOT HOW TO DO IT

Answer 19

Rationalize your root term using this rule:\[\Huge\rm \color{royalblue}{\sqrt[a]{x}}=x^{1/a}\]

Answer 20

SO 8^1/5?

Answer 21

Yes, good.
Let's do it to the top AND bottom ok?
\[\Large\rm \frac{\sqrt[2]{8}}{\sqrt[5]{8}}=\frac{8^{1/2}}{8^{1/5}}\]

Answer 22

WHERE DID YOU GET THE 2 FROM? THERE IS NO 2 IN THE QUESTION

Answer 23

When there is no index written on the root, it is implied to the `square` root, second root.

Answer 24

OH OKAY

Answer 25

implied to be the*

Answer 26

Then our rules of exponents tells us,\[\Large\rm \color{orangered}{\frac{x^a}{x^b}=x^{a-b}}\]

Answer 27

5/10-2/10?

Answer 28

RIGHT?

Answer 29

Mmm yes, good!

Answer 30

IM SORRY BUT CAN YOU TELL ME IF I GOT THIS ONE RIGHT?

Answer 31

Uh ohhhh I think you made a boo boo.

Answer 32

You've got the right idea,
since we're shifting to the `left`, we `add` to our x, yah?

But we're adding 13 to our x+1.

Answer 33

DANG! oh yeah I forgot about that, so its B?

Answer 34

because of the + 1?
yay good job \c:/

Answer 35

OKAY COOL :)

Answer 36

im working on a problem now once I formulate my answer can you check it for me?

Answer 37

@zepdrix okay, I got the numerator but I'm not sure about the denominator.

Answer 38

You got the numerator figured out?\[\Large\rm \sqrt[5]{8}\sqrt{8}=8^{1/5}\cdot 8^{1/2}=8^{1/5+1/2}=8^{7/10}\]That what you came up with for your numerator?

Answer 39

yes! :)

Answer 40

but what about the denominator?

Answer 41

Ohhh ok, lemme state the rule from earlier but with a power introduced.\[\Huge\rm \color{royalblue}{\sqrt[a]{x^b}}=x^{b/a}\]

Answer 42

is it c? 8^-29/30

Answer 43

yay good job \c:/

Answer 44

thanks, can we do another problem?

Answer 45

only like two more pretttty please?

Answer 46

you... -_-

Answer 47

no? lol okay I understand

Answer 48

i just want to make sure m doing it correctly

Answer 49

you..... you and your ways... -_-

Yah it's fine if I'm around c:
Just toss a @ if I'm not responding or whatev

Answer 50

okay thanks so much !!

Answer 51

its either B OR D, but im going with B

Answer 52

@zepdrix

Answer 53

NO D?

Answer 54

Do you remember the very first problem we did?
\[\Large\rm (1 +\color{orangered}{.0774})^x\]The orange represented the MORE each month.
The 1 + orange represents `the full amount + some more each month`

Answer 55

So if we have an increase of 5% each month,
next month she'll have 105% of her pop music from last month, yes?

Answer 56

YES

Answer 57

AND IN ORDER TO GET THAT MOVE CIMAL PLACE OVER BETWEEN THE 1 AND THE 0

Answer 58

BUT WAS I CORRECT?

Answer 59

lol those caps, simmer down :o

Answer 60

lol sorry, they don't mean anything

Answer 61

Which one did you go with?
Yah you need to move the decimal over to get the correct value, 1.05.

Just remember that since it's an `increase` we want the original amount + the 5%.
105%

Answer 62

D?

Answer 63

yes

Answer 64

OKAY! last one. this one i'm not sure how to do at all

Answer 65

@zepdrix

Answer 66

Oh yah this question is quite a bit harder than the previous ones.

So to find `rate of change` or `slope` we use the slope formula:

Answer 67

So in this case, we want to know how the function changed from year 1 to year 5.

Answer 68

\[\Large\rm \text{Change in students}=\frac{y_2-y_1}{x_2-x_1}\]Does that formula look familiar?

Answer 69

yes

Answer 70

We want to write it in function notation, which looks a little scarier.\[\Large\rm \frac{f(x_2)-f(x_1)}{x_2-x_1}\]And for this problem we're using this data:
\(\Large\rm x_1=1, \text{ first year}\)
\(\Large\rm x_2=5, \text{ fifth year}\)

Answer 71

\[\Large\rm \text{Change in students}=\frac{f(5)-f(1)}{5-1}\]

Answer 72

so is it just 1?

Answer 73

No.
f(5)-f(1) does not equal 4.

We have to calculate the function at these values.\[\Large\rm f(\color{orangered}{x})=11(1.35)^{\color{orangered}{x}}\]Evaluating the function at 5 gives us:\[\Large\rm f(\color{orangered}{5})=11(1.35)^{\color{orangered}{5}}\]Which simplifies to,\[\Large\rm f(\color{orangered}{5})\approx 49.3\]

Answer 74

Understand what I did to find f(5)?
Think you can figure out the f(1)?

Answer 75

yes, 14.85?

Answer 76

Ok great, so our rate of change we can write as,\[\Large\rm \text{Change in students}\approx \frac{49.32-14.85}{5-1}\]

Answer 77

8.6125?

Answer 78

Mmmmm yah I think we did that correctly.
That sounds about right :D

Answer 79

Remember, we're talking about students so we don't want to consider a `part of a student`.
We need to round to the nearest whole number.

Answer 80

so 9

Answer 81

cool c:

Answer 82

thank you so much !!!!!!!!!!

Answer 83

You might want to uhhh.. be more careful when you post your questions.
I think you can get in trouble for posting exam questions.
Either banned from the site and/or reported to flvs.

So either edit your pictures so it only includes the question, not the exam details at the top of the page and all that.

Or try to post questions from a practice test or something.

Answer 84

I don't really care that much, but I don't wanna see you get in twouble :O

Answer 85

okay thank you