Precalc honors math question help???

Question

please help I dont get this??? Thanks! And please explain how

Find the exponential function Ae^bx that passes though the two points : (0,2) (4,3)

because i just spent the last 15 minutes trying to and I can't figure it out!!! help???

Answer 1

The key here is that you're given the value for x = 0, and anything to the 0th power is 1.
f(x) = ae^bx
f(0) = 2 = ae^b(0)
0b = 0, and e^0 = 1.
That means that a = 2.

Now plug in a to the value for x = 4:
f(4) = 3 = 2e^b(4)
2e^4b = 3
e^4b = 3/2
ln e^4b = ln 1.5
4b = ln 1.5
b = ln 1.5 / 4 = 0.1013 (solution!)

Answer 2

I'm sorry, I saw that first answer, and I just had to post a real answer.

I say try to take it in parts. Like the first point, (0,2). Plug that in.
2 = Ae^(b X 0) = A X 1.

So now A is equal to 2, because e^0 = 1.
On to the next variable, that b. Same thing, plug in the points and see what happens, knowing A = 2.
3 = 2e^(4b), 3/2 = e^(4b), and now it gets a little hairy, because you have to solve it by pulling it apart and using natural log, like so:
ln(3/2) = 4b, b = ln(3/2)/4.

So your function is now: y = 2e^(xln(3/2)/4).


Sorry I can't simplify it, but there it is. Tricky part is probably the jump into the natural logs. Remember, e^a = b, so ln(b) = a.

Answer 3

why dont u find it smarty pants....u realize like only 1% o the ppl on yahoo can do this and thoes who can do this prolly dont wanna spend ny more time on it then they have 2