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.

- anonymous

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- Vocaloid

[ f(5)-f(1) ] / (5-1)
find f(5) and f(1), then plug them into the equation

- anonymous

Ok

- anonymous

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

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## More answers

- Vocaloid

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

- anonymous

16?

- Vocaloid

yeah! now find f(1)

- anonymous

256?

- Vocaloid

yup! now plug those values into our expression
[f(5)-f(1)] / (5-1)

- anonymous

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

- Vocaloid

uh, not quite, the f's go away when you replace them
(16-256) / (5-1) = ?

- anonymous

-60 would be the answer?

- Vocaloid

yup!

- anonymous

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

- Vocaloid

yeah! you got it

- anonymous

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

- Vocaloid

sure

- anonymous

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

- Vocaloid

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?

- anonymous

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

- Vocaloid

yeah, you got it ~

- anonymous

Ok 3 more

- anonymous

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)

- Vocaloid

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

- anonymous

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

- Vocaloid

yes

- anonymous

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

- anonymous

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

- Vocaloid

it's pretty much the same as the first problem you showed me
[ f(15)-f(12) ] / ( 15-12) = ?

- anonymous

I got 1 but it's not right

- Vocaloid

ok, let's take it step by step
f(15) = ?

- anonymous

x?

- Vocaloid

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

- anonymous

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

- Vocaloid

when you plug in 15, you replace "x" with 15
so f(15) = 0.01(2)^15

- anonymous

Oh ok

- Vocaloid

so, f(15) = ?

- anonymous

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

- anonymous

0.01(2)^15

- Vocaloid

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

- anonymous

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

- Vocaloid

you can use an online calculator

- Vocaloid

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

- anonymous

327.68

- Vocaloid

right, now find f(12)

- anonymous

40.96

- Vocaloid

right, now go back to the formula I gave you back then
[f(15)-f(12)] / (15-12) = ?

- anonymous

286.72

- anonymous

?

- Vocaloid

you still need to divide by (15-12)

- anonymous

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

- Vocaloid

you divide by 3

- anonymous

95.57?

- Vocaloid

yeah! that's our answer

- anonymous

Ok this ones a graph

- anonymous

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

- anonymous

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

- Vocaloid

can you try to draw what it looks like?

- anonymous

How do you draw it?

- Vocaloid

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

- Vocaloid

Is there a "draw" button anywhere?

- anonymous

Ok hold on

- anonymous

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.

- Vocaloid

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

- anonymous

Oh ok

- Vocaloid

the first one is the best choice here

- anonymous

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

- anonymous

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

- Vocaloid

great

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