anonymous
  • anonymous
Which of the following options results in a graph that shows exponential decay? f(x) = 0.6(2)x f(x) = 3(0.7)x f(x) = 0.4(1.6)x f(x) = 20(3)x
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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jim_thompson5910
  • jim_thompson5910
In general, the exponential function is \[\Large f(x) = a*b^x\] The base b determines if you have exponential growth or decay. If `0 < b < 1`, then you have exponential decay. If `b > 1`, then you have exponential growth.
jim_thompson5910
  • jim_thompson5910
For example, the function \[\Large f(x) = 33(2.7)^x\] has exponential growth because b = 2.7 is larger than 1.
anonymous
  • anonymous
Ok so for example f(x) = 3(0.7)to the x power is exponential decay @jim_thompson5910

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More answers

jim_thompson5910
  • jim_thompson5910
correct
jim_thompson5910
  • jim_thompson5910
since b = 0.7 is between 0 and 1 ie it makes `0 < b < 1` true
anonymous
  • anonymous
Ok thank you
jim_thompson5910
  • jim_thompson5910
np
anonymous
  • anonymous
Hey wait can you help me solve another problem? @jim_thompson5910
jim_thompson5910
  • jim_thompson5910
sure
jim_thompson5910
  • jim_thompson5910
go ahead
anonymous
  • anonymous
For f(x) = 0.01(2)to the x power, find the average rate of change from x=2 to x=10
jim_thompson5910
  • jim_thompson5910
are you able to determine f(2) ?
anonymous
  • anonymous
Nope that's all the question says
jim_thompson5910
  • jim_thompson5910
replace every x with 2 and evaluate the function
anonymous
  • anonymous
These are the choices: 1.275 8 10.2 10.24
jim_thompson5910
  • jim_thompson5910
ignore the choices for now
jim_thompson5910
  • jim_thompson5910
\[\Large f(x) = 0.01(2)^x\] \[\Large f(2) = 0.01(2)^2\] \[\Large f(2) = ??\]
anonymous
  • anonymous
0.04
jim_thompson5910
  • jim_thompson5910
yes
jim_thompson5910
  • jim_thompson5910
now evaluate f(10)
anonymous
  • anonymous
Ok
anonymous
  • anonymous
I got 1,024
jim_thompson5910
  • jim_thompson5910
you should get something smaller than that, try again
jim_thompson5910
  • jim_thompson5910
\[\Large f(x) = 0.01(2)^x\] \[\Large f(10) = 0.01(2)^{10}\] \[\Large f(10) = ??\]
anonymous
  • anonymous
10.24
jim_thompson5910
  • jim_thompson5910
better
anonymous
  • anonymous
Is that right
jim_thompson5910
  • jim_thompson5910
Last step: compute \[\Large \frac{f(b)-f(a)}{b-a}=\frac{f(10)-f(2)}{10-2} = ??\]
jim_thompson5910
  • jim_thompson5910
10.24 is not the answer, but it helps get you there
anonymous
  • anonymous
Wait is it 8over 8
jim_thompson5910
  • jim_thompson5910
\[\Large \frac{f(10)-f(2)}{10-2}=\frac{10.24-0.04}{10-2} = ??\]
anonymous
  • anonymous
Oh ok
anonymous
  • anonymous
So it 1.275
jim_thompson5910
  • jim_thompson5910
yes
anonymous
  • anonymous
And that's the right answer
jim_thompson5910
  • jim_thompson5910
yes
anonymous
  • anonymous
Ok thank you
jim_thompson5910
  • jim_thompson5910
np

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