Question

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?

Answer 1

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.

Answer 2

Does that make sense to you?

Answer 3

Try solving the system and tell me what you get.

Answer 4

ok, I'll try.

Answer 5

Start by substituting a=8/b^4 into the second equation.

Answer 6

8/b^4 ^b6 ?

Answer 7

Hmm. From the first equation we have:
\[8=a.b^4 \implies a={8 \over b^4} \rightarrow (3)\]

Answer 8

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.

Answer 9

Are you following so far?

Answer 10

yes, I'm looking.

Answer 11

Now just substitute in (3) by the value of x. You will get a=1/2.

Answer 12

make sure to keep your eyes open O_O

Answer 13

So, we have, from equation (3), a=8/b^4, and b=2 or -2. Then:
\[a={8 \over 2^4}={8 \over 16}=1/2\]

Answer 14

Your equation should be one of two (since you have two values for b):
\[1) y={1 \over 2}(2)^x \implies 2y=2^x\]

Answer 15

The second equation is the same, but with (-2)^x.

Answer 16

Thanks for your help. I'm going to need a lot of practice with exploring exponential models.

Answer 17

Good luck!! :)