anonymous
  • anonymous
If f is an exponential funtion with the values of f (1)=4 & f (6)=7, Find F(16)
Algebra
schrodinger
  • schrodinger
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SolomonZelman
  • 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) \(\large\color{blue}{ \displaystyle 6=a(b)^7 }\) \(\large\color{blue}{ \displaystyle 4=a(b)^1 }\)
SolomonZelman
  • 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.
SolomonZelman
  • 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.

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anonymous
  • 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
anonymous
  • anonymous
I have trouble with math allot sorry
SolomonZelman
  • 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...
anonymous
  • anonymous
So I use 6,7?
SolomonZelman
  • SolomonZelman
What do you mean to use (6, 7) ?
SolomonZelman
  • SolomonZelman
yeah mistake
SolomonZelman
  • SolomonZelman
I saw it while you were typing, tnx for mentioning it
anonymous
  • 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
SolomonZelman
  • 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)
SolomonZelman
  • SolomonZelman
The system should be: \(\large\color{blue}{ \displaystyle 7=a(b)^6 }\) \(\large\color{blue}{ \displaystyle 4=a(b)^1 }\)
SolomonZelman
  • SolomonZelman
do u understand the correction I made?
anonymous
  • anonymous
Yes
anonymous
  • anonymous
Now that we have that whats next
SolomonZelman
  • 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 \(\large\color{blue}{ \displaystyle 7=4(b)^{-1}(b)^6 }\) \(\large\color{blue}{ \displaystyle 7/4=(b)^{5} }\) \(\large\color{blue}{ \displaystyle b=\sqrt[5]{7/4} }\)
SolomonZelman
  • SolomonZelman
and then find a, using the value of b.
anonymous
  • anonymous
Kk but i dont underatand how this will help me find f(16)
anonymous
  • anonymous
?
courtneygraley009
  • 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.

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