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

Question

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

solomonzelman · Answer

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 · Answer

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 · Answer

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.

anonymous · Answer

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 · Answer

I have trouble with math allot sorry

solomonzelman · Answer

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 · Answer

So I use 6,7?

solomonzelman · Answer

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

solomonzelman · Answer

yeah mistake

solomonzelman · Answer

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

anonymous · Answer

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 · Answer

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

solomonzelman · Answer

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

solomonzelman · Answer

do u understand the correction I made?

anonymous · Answer

Yes

anonymous · Answer

Now that we have that whats next

solomonzelman · Answer

$\large\color{blue}{ \displaystyle 7=a(b)^6 }$
$\large\color{blue}{ \displaystyle 4=a(b)^1 }$

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 · Answer

and then find a, using the value of b.

anonymous · Answer

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

anonymous · Answer

?

courtneygraley009 · Answer

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.