anonymous
  • anonymous
Question says, "Write an exponential function y=ab^x for a graph that includes the given points. (4,8), (6,32) How do I do this?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
Deal with the problem as a system of 2 equations in two unknowns. The two equations are: \[8=a. {b^4} \rightarrow(1)\] \[32=a.b^6 \rightarrow(2)\] Now, find the two unknowns a and b.
anonymous
  • anonymous
Does that make sense to you?
anonymous
  • anonymous
Try solving the system and tell me what you get.

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anonymous
  • anonymous
ok, I'll try.
anonymous
  • anonymous
Start by substituting a=8/b^4 into the second equation.
anonymous
  • anonymous
8/b^4 ^b6 ?
anonymous
  • anonymous
Hmm. From the first equation we have: \[8=a.b^4 \implies a={8 \over b^4} \rightarrow (3)\]
anonymous
  • anonymous
Now, take this value of a and substitute it in (2), you get: \[32=a. b^6 \implies 32={8 \over b^4}.b^6 \implies 8b^2=32 \implies b^2=4\] So, b is either 2 or -2.
anonymous
  • anonymous
Are you following so far?
anonymous
  • anonymous
yes, I'm looking.
anonymous
  • anonymous
Now just substitute in (3) by the value of x. You will get a=1/2.
anonymous
  • anonymous
make sure to keep your eyes open O_O
anonymous
  • anonymous
So, we have, from equation (3), a=8/b^4, and b=2 or -2. Then: \[a={8 \over 2^4}={8 \over 16}=1/2\]
anonymous
  • anonymous
Your equation should be one of two (since you have two values for b): \[1) y={1 \over 2}(2)^x \implies 2y=2^x\]
anonymous
  • anonymous
The second equation is the same, but with (-2)^x.
anonymous
  • anonymous
Thanks for your help. I'm going to need a lot of practice with exploring exponential models.
anonymous
  • anonymous
Good luck!! :)

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