Question

gg

Answer 1

@sooobored

Answer 2

so what do you not understand?

Answer 3

whole thing.....

Answer 4

ok,
firstly,
f(x) - denotes a function or is the way of saying, "this equation is a function"

Answer 5

\[f(x) = a(b)^x\]
and
\[f(x)= P(1+r)^x\]
are both different forms of exponential functions

Answer 6

notice how the 2 equations are similar if you set
a = P and b= 1+r

Answer 7

first first form is the more general exponential function

the 2nd form is used mostly when calculating compound interest problems

Answer 8

any questions thus far?

Answer 9

uh yeah ... what do i write down into my notebook?

Answer 10

oh nothing yet okay

Answer 11

uhhh, whatever you think is important?

Answer 12

okay so what am i suppose to think of?

Answer 13

i do not know what you are saying

the 2 functions are very basic forms which would be immensely helpful if memorized

Answer 14

from what you showed, it defines that a is the y-intercept
where the y-intercept is the point on the y-axis having the form (0,a)

Answer 15

No i understand but what is exactly my homework?

Answer 16

there is no homework from what you showed me

Answer 17

because imr eading it and cant understand whats its asking me

Answer 18

Oh are you serious

Answer 19

its all basic information and definitions

Answer 20

WAIT !!!! I got it ooops!

Answer 21

i dont see any question marks hence no questions

Answer 22

those are the questions

Answer 23

number 1 is asking you to write down a function for the population of snails
since it states that the growth is exponential, the function of population would be an exponential function

then explain what the variables you wrote down mean in complete sentences

Answer 24

okay i see

Answer 25

if we are to consider population and time into a coordinate system, we would make the x-axis as time (years since its asking for growth over 15 years, you could do months in which case it would be 600 months)

and y-axis would be total population of snails, since that is changing over time

Answer 26

so which of the 2 forms of exponential functions would you use?
and what would the variables mean in your snail case?

Answer 27

f(x)=a(b)^x

Answer 28

ok, and what is the meaning of a?

Answer 29

Snails

Answer 30

not specific enough

Answer 31

as the basic information stated, a is the y-intercept
in our snails case, this means the point (0,a)
meaning at time 0 the population of snail is a

thus "a" must mean the initial population of snails we started with

Answer 32

ok, what does b mean?

Answer 33

OH okay

Answer 34

B means decreasing of snails

Answer 35

or wait

Answer 36

B is rate of growth sorry

Answer 37

yes, rate of growth,

if i said that the population doubles every year, what value would b be?

Answer 38

rate of growth still?

Answer 39

what number- value

Answer 40

b=?
if i said teh population is doubling every year

Answer 41

b= doubled rate of growth .

Answer 42

no,
b=2

Answer 43

wa

Answer 44

if the population tripled every year, b=3
quadrupled b=4

Answer 45

does this make some sense, or do you totally not understand?

Answer 46

oh okay i see!

Answer 47

I totally understand

Answer 48

so i can write tht b=1 and or b= rate of growth

Answer 49

no
b=1 means that population wouldnt change from year to year

since you multiply the initial population by this rate "b"

Answer 50

Oh okay is see why not

Answer 51

assuming we start with a population of "a" snails
after the first year, we would have b*a snails
after the 2nd, we would have b*b*a snails
3rd, b*b*b*a

Answer 52

etc

Answer 53

yeha i get it

Answer 54

ok side questions, if i said the population was half every year, then what would the rate be?

Answer 55

for #2 i would pick f(x)=a(b)^x

Answer 56

#2 is asking something totally different

Answer 57

b=100 something?

Answer 58

still on #1

Answer 59

population is being halved every year, b=?

Answer 60

b=100 something

Answer 61

or no 6

Answer 62

or -6

Answer 63

being halved means that population is decreasing
100 ->50-25-12.5 ...

so why wouldnt it be b=1/2 ?

Answer 64

because half a year doesnt mean 1/2

Answer 65

it means 6

Answer 66

no no, being halved per year

every year, the population is divided by 2

Answer 67

if we assume every x unit is a year

then after year 1, then we would divide the total pop by 2 or multiply by 1/2

Answer 68

b is the value in which you modify the initial population by

Answer 69

oh

Answer 70

if its growing, b is greater than 1
if its decreasing, b is less than 1 but greater than 0

Answer 71

if b is negative, then that doesnt make any sense in our problem,
how can you have a negative amount of snails?
and then have a positive amount of snails the next year?

Answer 72

ok, i think i've explained enough to thoroughly answer #1

any questions?

Answer 73

i dont think so after that explanation

Answer 74

not in bad way but good way

Answer 75

ok
your question number 2
is an application of
power of a power property

read through that and then tell me if you still dont know how to do #2

Answer 76

so i wrote
A= population of snails
B= rate of change
x= (not sure)

Answer 77

x is the year

after 1 year- you would set x=1 and solve for the total population f(1)
after 2 years- you would set x=2 and solve for the total population f(2)
3 years
4 years
etc

Answer 78

the 15 years doesnt mean much,the function you wrote down gives you the total population after x years

if you wanted to solve the population after 15 years, you would set x=15 and find f(15)

Answer 79

oh so should i write down x= years in rate of growth

Answer 80

x would the the number of years that pass
it has nothing to do with rate of growth

Answer 81

okay mvoing to number 2

Answer 82

right, as i said, application of power of power rule
read through that, read through taht question
try to figure it out,
show me steps,
and if you still dont understand, say something

Answer 83

question is asking you to make the power x instead of 2x

Answer 84

yeah nore sure how.. but my teacher went over this a bit i think

Answer 85

wouldn't we multiply 1.03*2 and then the outcme would be 2.06^2

Answer 86

2.06^x

Answer 87

close

but you dont multiply

Answer 88

divide?

Answer 89

"power" of "power"

Answer 90

what does tht mean?

Answer 91

ok, so the power of power property says
if you have a power to a power

then instead of taking the power to the power

you can multiply them instead

so \[n^{x^y} = n^{xy}\]

Answer 92

uuuh

Answer 93

not familiar with that

Answer 94

but it also means that you can group them
so commutative property \[xy=yx\]

and
\[(n^x)^y = n^{xy}= (n^y)^x\]

Answer 95

what i wrote above is an extension of the power to power property that was not clearly defined in whatever material is given to you

Answer 96

remember that rule

an exponent to an exponent is the equivalent of multiplying the two exponent numbers together