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I would like to know what the equation of a curve is if it grows exponentially (let's say it doubles each time). This would be:

$f(x)=2^x$

But then I would like the line to exponentially decay (let it half each time once it reaches let's say 7) with an asymptote of 10.

How could I write this equation? I am only a sophomore in high school right now taking Pre-IB Algebra II by the way.

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  • $\begingroup$ wolframalpha.com/input/?i=x%5E2 $\endgroup$ – Belgi Dec 4 '14 at 20:57
  • $\begingroup$ graphing can be done by $(x,f(x))$. Doubling every time would be $2^x$ $\endgroup$ – tp1 Dec 4 '14 at 20:57
  • $\begingroup$ @tp1 oh yeah my mistake! Thanks for pointing it out btw $\endgroup$ – zzirrgrizz Dec 4 '14 at 20:59
  • $\begingroup$ Not quite what you're expecting, but what about $7\cdot2^{-(x-3)^2}$ ? $\endgroup$ – Lucian Dec 4 '14 at 22:07
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Since your curve does two very different things on the two intervals, you will need to define a piecewise function.

When $x \leq 7$, your function would be $f(x)$ = $2^x$

When $x > 7$, your function would be $f(x)$ = ${0.5}^x + 10$.

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  • $\begingroup$ Sorry btw, I fixed that $x^2$ mistake! I must have been typing too fast $\endgroup$ – zzirrgrizz Dec 4 '14 at 21:01
  • $\begingroup$ By the way, is there anyway to get anything similar to this all in one equation? $\endgroup$ – zzirrgrizz Dec 4 '14 at 21:05
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    $\begingroup$ @zzirrgrizz $f(x) = 2^{7-|x-7|}$. $\endgroup$ – user147263 Dec 4 '14 at 21:17

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