How do you find an exponential function given the points are (-1,8) and (1,2)?

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How do you find an exponential function given the points are (-1,8) and (1,2)?

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Answer 1 · 2016-01-09T00:37:31

$y=4(1/2)^x$

Explanation:

An exponential function is in the general form

$y=a(b)^x$

We know the points $(-1,8)$ and $(1,2)$ , so the following are true:

$8=a(b^-1)=a/b$

$2=a(b^1)=ab$

Multiply both sides of the first equation by $b$ to find that

$8b=a$

Plug this into the second equation and solve for $b$ :

$2=(8b)b$

$2=8b^2$

$b^2=1/4$

$b=+-1/2$

Two equations seem to be possible here. Plug both values of $b$ into the either equation to find $a$ . I'll use the second equation for simpler algebra.

If $b=1/2$ :

$2=a(1/2)$

$a=4$

Giving us the equation: $color(green)(y=4(1/2)^x$

If $b=-1/2$ :

$2=a(-1/2)$

$a=-4$

Giving us the equation: $y=-4(-1/2)^x$

However! In an exponential function, $b>0$ , otherwise many issues arise when trying to graph the function.

The only valid function is

$color(green)(y=4(1/2)^x$

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How do you find an exponential function given the points are (-1,8) and (1,2)?

1 Answer

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