## anonymous one year ago If f is an exponential funtion with the values of f (1)=4 & f (6)=7, Find F(16)

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1. SolomonZelman

You have two points: (1,4) and (6,7) An exponential function is in the form of $$y=a(b)^x$$ and with these two given points you can solve for a and b. (just plug these points in and make a system of equations to solve) $$\large\color{blue}{ \displaystyle 6=a(b)^7 }$$ $$\large\color{blue}{ \displaystyle 4=a(b)^1 }$$

2. SolomonZelman

After you find a and b, plug them into the function $$\large\color{blue}{ \displaystyle y=a(b)^x }$$, and this will give you the full function.

3. SolomonZelman

Lastly, you need to find f(16), so plug in 16 for x into your new function (after finding a and b), and there is going to be the answer.

4. anonymous

Omg thank you so much for replying but what would be my a and b that i would have to plug in to solve

5. anonymous

I have trouble with math allot sorry

6. SolomonZelman

You can make a substitution. Rearrange one of the equations (I would adive the second one) for a in terms of b or vice versa and substitute...

7. anonymous

So I use 6,7?

8. SolomonZelman

What do you mean to use (6, 7) ?

9. SolomonZelman

yeah mistake

10. SolomonZelman

I saw it while you were typing, tnx for mentioning it

11. anonymous

You know the points i was given 1,4 and 6,7 you said it would be easier to use the 2nd set of points oh ok what was rhw mistake

12. SolomonZelman

$$\large\color{blue}{ \displaystyle 7=a(b)^6 }$$ (the y-value is 7 and the x-value is 6) (the way I posted it before, it was the other way around)

13. SolomonZelman

The system should be: $$\large\color{blue}{ \displaystyle 7=a(b)^6 }$$ $$\large\color{blue}{ \displaystyle 4=a(b)^1 }$$

14. SolomonZelman

do u understand the correction I made?

15. anonymous

Yes

16. anonymous

Now that we have that whats next

17. SolomonZelman

$$\large\color{blue}{ \displaystyle 7=a(b)^6 }$$ $$\large\color{blue}{ \displaystyle 4=a(b)^1 }$$ from the second equation, 4=ab >> 4/b=a >> 4b$$^{-1}$$=a $$\large\color{blue}{ \displaystyle 7=4(b)^{-1}(b)^6 }$$ $$\large\color{blue}{ \displaystyle 7/4=(b)^{5} }$$ $$\large\color{blue}{ \displaystyle b=\sqrt[5]{7/4} }$$

18. SolomonZelman

and then find a, using the value of b.

19. anonymous

Kk but i dont underatand how this will help me find f(16)

20. anonymous

?

21. courtneygraley009

Try http://www.acalculator.com/exponential-equations-calculator.html online tool to calculate the exponential equation. This tools is free, easy to understand and gives 100% accurate result.