Question

I need help on a question for exponential functions: Which of these constants could possibly be greater than the value of a?

Answer 1

do u have options for this ?

Answer 2

No, I don't that's. all he gave me

Answer 3

I'm suppose to enter in the letter's from the equations that, given the shape of the graph could be larger then a. I have tried multiple combinations and all of them have been wrong.

Answer 4

that is all I have ^

Answer 5

@ganeshie8 any ideas?

Answer 6

Now it makes more sense :)

Answer 7

Notice that all graphs are cutting the positive y axis,
that means `p, a, c` will be positive for sure

Answer 8

since the green graph is rising, `q` also will be positive

Answer 9

so, overall `p,a,c,q` are positive for sure.

Answer 10

see if that makes more or less sense...

Answer 11

wouldn't b and d be positive too, just less then 1?

Answer 12

very good catch :) yes ! all are positive then ?

Answer 13

so which are greater then a if all of them are greater then 0?

Answer 14

I know at least 1 or more of c,d,b,p, and q are less then a

Answer 15

clearly `c, p` are less than `a`,
so eliminate them first

Answer 16

try `q,b,d`

Answer 17

how do you know c and p are less then a?

Answer 18

c, p, a are y-intercepts of graphs right ?

Answer 19

notice that y-intercepts of blue and green graphs are below the y-intercept of green graph

so, c and p are less than a

Answer 20

oh, okay that makes more sense. He kind of confused me because he gave us this:

Answer 21

and said that was all we needed to know to do all the homework but never explained anything

Answer 22

lol thats tricky, but he is true ;) thats all is ever needed if u have 10 hours to work on it trying to figure out ...

Answer 23

yeah...just looking at the diagram he gave us, its easy to assume that c>a in the homework because g>e in the diagram. he never explained anything about the y axis playing a part

Answer 24

yes :) C>A because C graph is cutting the y axis a bit higher than the A graph

Answer 25

I meant c in the homework not in my diagram i drew lol

Answer 26

ahh okay got u :)

Answer 27

Do you have any advice on this one as well?

Answer 28

its really hard to tell because if i click one wrong one or dont click one that's suppose to be clicked its all marked wrong so I can't figure out how to know which ones would be right and which would be wrong

Answer 29

first start by figuring out the y-intercept of e^x (blue graph)

Answer 30

y intercept occurs when x = 0, right ?

Answer 31

so,
y intercept of e^x = e^0 = 1

Answer 32

that means, the value at which the `blue curve` cuts the y axis is `1`

Answer 33

fien ?

Answer 34

*fine

Answer 35

okay, that makes sense

Answer 36

and since red and green are cutting the y axis at same place,

a = b

Answer 37

and a > 1 and b > 1 also

Answer 38

so a = 1 is wrong.

Answer 39

you need to tick ur second option.
b > 1 is correct

Answer 40

what do you mean trick your second option?

Answer 41

sorry, i meant to select ur second option.

Answer 42

k > 1 is also correct since the green graph is rising.

Answer 43

oh okay hah that makes more sense

Answer 44

that makes the D wrong.

Answer 45

and since we already know that a = b, option E is also wrong

Answer 46

and 0<n<1 right?

Answer 47

because it decays?

Answer 48

lets go thru the options one by one okay ?

Answer 49

k

Answer 50

So far we have :

```
A : false
B : true
C : true
D : false
E : false
```

Answer 51

and ur recent observation on `n` makes the F option wrong

Answer 52

```
A : false
B : true
C : true
D : false
E : false
F : false
```

Answer 53

fine so far ha ?

Answer 54

yup!

Answer 55

G is false as we figured out already that b > 1

Answer 56

H is true

Answer 57

I is also true

Answer 58

So :



```
A : false
B : true
C : true
D : false
E : false
F : false
G : false
H : true
I : true
```

Answer 59

still fine ?

Answer 60

yup

Answer 61

actually the exponent "n" needs to be negative to get a declining graph

Answer 62

now you lost me..

Answer 63

I thought it just had to be less then 1 but still greater then 0?

Answer 64

\(\large y = e^{0.01x}\) is a rising graph

Answer 65

so that only applies to when the base is 0<base<1?

Answer 66

http://prntscr.com/3dhcyw

Answer 67

ok

Answer 68

so right now we have BCHIK true?

Answer 69

We were actually wrong, C was false because K had to be less than 1.

Answer 70

Correct ! k>0 is sufficient

Answer 71

lets change the answers lol

Answer 72

we were wrongly thinking k needs to be greater than 1

Answer 73

and that makes k to be between 0 and 1
so D is true

Answer 74

try this

```
A : false
B : true
C : false
D : true
E : false
F : false
G : false
H : true
I : true
J : false
K : true
L : false
M : false
N : false
N : false
```

Answer 75

Yup! I got those when I figured out c was wrong and plugged them all in and they were correct

Answer 76

yaay ! nice :)

Answer 77

Thanks much! :D I'll let you know If I run across anymore that stump me. It's due in an hour so if you don't hear from me by then it means I understood the rest of it :P