Question

Need help a chess competition has eliminations each round. The table below shows the number of players in each of the first 5 rounds of tournament
Round(x) Players f(x)
1 256
2 128
3 64
4 32
5 16

Compute the average rate of change of f(x) from x = 1 to x = 5 identify the meaning of that rate.

Answer 1

[ f(5)-f(1) ] / (5-1)

find f(5) and f(1), then plug them into the equation

Answer 2

Ok

Answer 3

I'm terrible at math can explain how to do the problem

Answer 4

what is f(5)? (look at the table)

Answer 5

16?

Answer 6

yeah! now find f(1)

Answer 7

256?

Answer 8

yup! now plug those values into our expression

[f(5)-f(1)] / (5-1)

Answer 9

F(16)-f(256)/ (5-1)?

Answer 10

uh, not quite, the f's go away when you replace them

(16-256) / (5-1) = ?

Answer 11

-60 would be the answer?

Answer 12

yup!

Answer 13

So it would be -60; on average, there was a loss of 60 each round?

Answer 14

yeah! you got it

Answer 15

Thank you! Can you help me with a few more?

Answer 16

sure

Answer 17

Ok which of the following options results in a graph that shows exponential growth?
f(x) = 0.4(0.2)^x
f(x) = 4(0.98)^x
f(x) = 0.7(5)^x
f(x) = 5(4)^-x

Answer 18

2 requirements for exponential growth:

1. the exponent must be positive
2. the ratio (the number in parentheses) must be greater than 1

given this information, which of the four choices do you think it is?

Answer 19

F(x) = 0.7(5)^x?

Answer 20

yeah, you got it ~

Answer 21

Ok 3 more

Answer 22

Which of the following options is an equivalent function to f(x) = 4(3)^2x
f(x) = 36^x
f(x) = 4(9)^x
f(x) = 144^x
f(x) = 4(6x)

Answer 23

you can simplify (3^2)^x to 9^x, but you have to leave the 4 alone since it's not attached to the x

f(x) = 4(9)^x

Answer 24

Wait f(x) = 4(9)^x is the answer?

Answer 25

yes

Answer 26

Oh ok I would say explain but it seems you already did ok 2 more

Answer 27

For f(x) = 0.01(2)^x, find the average rate of change from x = 12 and x = 15

3
40.96
95.57
286.72

Answer 28

it's pretty much the same as the first problem you showed me

[ f(15)-f(12) ] / ( 15-12) = ?

Answer 29

I got 1 but it's not right

Answer 30

ok, let's take it step by step

f(15) = ?

Answer 31

x?

Answer 32

f(x) = 0.01(2)^x
f(15) = ?

Answer 33

I'm confused I'm so bad at math so your plugging in the 15 so it's f(15) = 0.01(2)^x?

Answer 34

when you plug in 15, you replace "x" with 15

so f(15) = 0.01(2)^15

Answer 35

Oh ok

Answer 36

so, f(15) = ?

Answer 37

So what do you do with f(15) = 0.01(2)^15

Answer 38

0.01(2)^15

Answer 39

just type it out on a calculator and tell me what you get

Answer 40

I don't have that calculator I have to find it

Answer 41

you can use an online calculator

Answer 42

https://www.bing.com/search?q=0.01(2)%5E15&PC=U316&FORM=CHROMN

Answer 43

327.68

Answer 44

right, now find f(12)

Answer 45

40.96

Answer 46

right, now go back to the formula I gave you back then

[f(15)-f(12)] / (15-12) = ?

Answer 47

286.72

Answer 48

?

Answer 49

you still need to divide by (15-12)

Answer 50

I did I divided 286.72 by 286.72 and I got 1 or do you divide 286.72 by 3

Answer 51

you divide by 3

Answer 52

95.57?

Answer 53

yeah! that's our answer

Answer 54

Ok this ones a graph

Answer 55

Identify the domain of the exponential function shown in the following graph:

All real numbers
All positive numbers
1 less than or equal to x less than or equal to 30
All integers

Answer 56

Idk how to to add the graph I'm on my phone

Answer 57

can you try to draw what it looks like?

Answer 58

How do you draw it?

Answer 59

I'm not sure what you would do on a phone

Answer 60

Is there a "draw" button anywhere?

Answer 61

Ok hold on

Answer 62

A curve runs just above the x axis through the second quadrant, passes through point 0 comma 1 and continues off screen near 1 comma 12.

Answer 63

it seems like the domain would be all real values since there aren't any gaps or asymptotes

Answer 64

Oh ok

Answer 65

the first one is the best choice here

Answer 66

I can try attach the graph if it would help strengthen the answer

Answer 67

No need I got them all right thank you!!!

Answer 68

great