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anonymous
 5 years ago
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?
anonymous
 5 years ago
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?

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Deal 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
 5 years ago
Best ResponseYou've already chosen the best response.0Does that make sense to you?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Try solving the system and tell me what you get.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Start by substituting a=8/b^4 into the second equation.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Hmm. From the first equation we have: \[8=a.b^4 \implies a={8 \over b^4} \rightarrow (3)\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Now, 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
 5 years ago
Best ResponseYou've already chosen the best response.0Are you following so far?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Now just substitute in (3) by the value of x. You will get a=1/2.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0make sure to keep your eyes open O_O

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So, 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
 5 years ago
Best ResponseYou've already chosen the best response.0Your 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
 5 years ago
Best ResponseYou've already chosen the best response.0The second equation is the same, but with (2)^x.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Thanks for your help. I'm going to need a lot of practice with exploring exponential models.
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