anonymous
  • anonymous
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.
Mathematics
schrodinger
  • schrodinger
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Vocaloid
  • Vocaloid
[ f(5)-f(1) ] / (5-1) find f(5) and f(1), then plug them into the equation
anonymous
  • anonymous
Ok
anonymous
  • anonymous
I'm terrible at math can explain how to do the problem

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Vocaloid
  • Vocaloid
what is f(5)? (look at the table)
anonymous
  • anonymous
16?
Vocaloid
  • Vocaloid
yeah! now find f(1)
anonymous
  • anonymous
256?
Vocaloid
  • Vocaloid
yup! now plug those values into our expression [f(5)-f(1)] / (5-1)
anonymous
  • anonymous
F(16)-f(256)/ (5-1)?
Vocaloid
  • Vocaloid
uh, not quite, the f's go away when you replace them (16-256) / (5-1) = ?
anonymous
  • anonymous
-60 would be the answer?
Vocaloid
  • Vocaloid
yup!
anonymous
  • anonymous
So it would be -60; on average, there was a loss of 60 each round?
Vocaloid
  • Vocaloid
yeah! you got it
anonymous
  • anonymous
Thank you! Can you help me with a few more?
Vocaloid
  • Vocaloid
sure
anonymous
  • 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
  • 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
  • anonymous
F(x) = 0.7(5)^x?
Vocaloid
  • Vocaloid
yeah, you got it ~
anonymous
  • anonymous
Ok 3 more
anonymous
  • 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
  • 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
  • anonymous
Wait f(x) = 4(9)^x is the answer?
Vocaloid
  • Vocaloid
yes
anonymous
  • anonymous
Oh ok I would say explain but it seems you already did ok 2 more
anonymous
  • 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
  • Vocaloid
it's pretty much the same as the first problem you showed me [ f(15)-f(12) ] / ( 15-12) = ?
anonymous
  • anonymous
I got 1 but it's not right
Vocaloid
  • Vocaloid
ok, let's take it step by step f(15) = ?
anonymous
  • anonymous
x?
Vocaloid
  • Vocaloid
f(x) = 0.01(2)^x f(15) = ?
anonymous
  • 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
  • Vocaloid
when you plug in 15, you replace "x" with 15 so f(15) = 0.01(2)^15
anonymous
  • anonymous
Oh ok
Vocaloid
  • Vocaloid
so, f(15) = ?
anonymous
  • anonymous
So what do you do with f(15) = 0.01(2)^15
anonymous
  • anonymous
0.01(2)^15
Vocaloid
  • Vocaloid
just type it out on a calculator and tell me what you get
anonymous
  • anonymous
I don't have that calculator I have to find it
Vocaloid
  • Vocaloid
you can use an online calculator
Vocaloid
  • Vocaloid
https://www.bing.com/search?q=0.01(2)%5E15&PC=U316&FORM=CHROMN
anonymous
  • anonymous
327.68
Vocaloid
  • Vocaloid
right, now find f(12)
anonymous
  • anonymous
40.96
Vocaloid
  • Vocaloid
right, now go back to the formula I gave you back then [f(15)-f(12)] / (15-12) = ?
anonymous
  • anonymous
286.72
anonymous
  • anonymous
?
Vocaloid
  • Vocaloid
you still need to divide by (15-12)
anonymous
  • anonymous
I did I divided 286.72 by 286.72 and I got 1 or do you divide 286.72 by 3
Vocaloid
  • Vocaloid
you divide by 3
anonymous
  • anonymous
95.57?
Vocaloid
  • Vocaloid
yeah! that's our answer
anonymous
  • anonymous
Ok this ones a graph
anonymous
  • 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
  • anonymous
Idk how to to add the graph I'm on my phone
Vocaloid
  • Vocaloid
can you try to draw what it looks like?
anonymous
  • anonymous
How do you draw it?
Vocaloid
  • Vocaloid
I'm not sure what you would do on a phone
Vocaloid
  • Vocaloid
Is there a "draw" button anywhere?
anonymous
  • anonymous
Ok hold on
anonymous
  • 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
  • Vocaloid
it seems like the domain would be all real values since there aren't any gaps or asymptotes
anonymous
  • anonymous
Oh ok
Vocaloid
  • Vocaloid
the first one is the best choice here
anonymous
  • anonymous
I can try attach the graph if it would help strengthen the answer
anonymous
  • anonymous
No need I got them all right thank you!!!
Vocaloid
  • Vocaloid
great

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