anonymous
  • anonymous
I think it is C, am i right? 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
Mathematics
schrodinger
  • schrodinger
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jim_thompson5910
  • jim_thompson5910
why C?
anonymous
  • anonymous
i really dont know, i think it is also B as well
jim_thompson5910
  • jim_thompson5910
Rule: If you have \[\Large f(x) = a*(b)^x\] f(x) will have exponential growth if `b > 1` or f(x) will have exponential decay if `0 < b < 1`

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anonymous
  • anonymous
so it is neither C or B..
jim_thompson5910
  • jim_thompson5910
Flip things around If you have \[\Large f(x) = a*(b)^{-x}\] f(x) will have exponential decay if `b > 1` or f(x) will have exponential growth if `0 < b < 1`
jim_thompson5910
  • jim_thompson5910
which function has `b > 1` ? and has `x` (not `-x`) in the exponent?
anonymous
  • anonymous
it has to be A then
jim_thompson5910
  • jim_thompson5910
in choice A, what are the values of a and b?
anonymous
  • anonymous
8
jim_thompson5910
  • jim_thompson5910
for `f(x) = 0.4(0.2)^x`, the value of a and b are a = 0.4 b = 0.2 agreed?
anonymous
  • anonymous
oh yes, im sorry i miss read what you said.
jim_thompson5910
  • jim_thompson5910
so b = 0.2 is b > 1 true?
anonymous
  • anonymous
i think it is
jim_thompson5910
  • jim_thompson5910
0.2 > 1 is true?
jim_thompson5910
  • jim_thompson5910
here is a graph to interactively play with https://www.desmos.com/calculator/fhg9iipwt0
jim_thompson5910
  • jim_thompson5910
adjust the sliders for 'a' and 'b'. Make sure 'a' stays as a positive number
anonymous
  • anonymous
a stayed as a positive number @jim_thompson5910
jim_thompson5910
  • jim_thompson5910
yeah make a = 2 or something then adjust the slider for b
anonymous
  • anonymous
they stayed positive @jim_thompson5910

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