## 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?

1. 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.

2. anonymous

Does that make sense to you?

3. anonymous

Try solving the system and tell me what you get.

4. anonymous

ok, I'll try.

5. anonymous

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

6. anonymous

8/b^4 ^b6 ?

7. anonymous

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

8. 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.

9. anonymous

Are you following so far?

10. anonymous

yes, I'm looking.

11. anonymous

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

12. anonymous

make sure to keep your eyes open O_O

13. anonymous

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

14. anonymous

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

15. anonymous

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

16. anonymous

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

17. anonymous

Good luck!! :)