Posted by Jim on Tuesday, December 1, 2009 at 12:47am.
I need to write 2 equations that represent the same exponential function with a yintercept of 5 and an asymptote at y=3. I got y=2^(x+1) + 3 but I don't know how to find the second equation. Can someone please explain this to me. Thanks.

Math  Reiny, Tuesday, December 1, 2009 at 8:54am
I don't know at what level you are working at, but any exponential of the form y = p^x can be written as
y = a(e^kx) where a and k are constants.
So let your y=2^(x+1) + 3 be
y = a(e^kx) + 3
let's use 2 points from your first equation, say (0,5) and (1,7)
in the new one:
for (0,5) ,
5 = a(e^0) + 3
a = 2
for (1,7)
7 = 2(e^k) + 3
2 = e^k
k = ln2
so a second equation would be
y = 2(e^[(ln2)x)] + 3
check it by using (2,11) from the first equation and trying it in our new one.
LS = 11
RS = 2(e^2ln2) + 3
= 2(e^1.386294361) + 3
= 2(4) + 3
= 11
= RS

Math  Jim, Tuesday, December 1, 2009 at 1:23pm
Thank you so much for your detailed reply. My problem is that we haven't done logs or "e" yet. Is there any other way arrive at an answer without knowing these? I really appreciate your help.
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