Let F(x)=12/3+ae^kx with f(0)=2 and f(1)=1/2
The value of a is ____???
The value of k is ____????
F(3)_____????
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I solved 12/3 + aekx
When the question SHOULD have read 12 / ( 3+aekx) Use the correct syntax people ! It IS VERY IMPORTANT !!!!
See Chris' answer below
I think this is supposed to be a logistics growth/decay equation.....we have that
12
f(x) = _________
a + e^(kx)
We know that f(0) = 2 this makes e^(kx) = e^(k*0) = 1
So
12
2 = _____
a + 1
Means that a = 5
And f(1) = 1/2 ....so.......
12
1/2 = _________ rearrange as
5 + e^(k)
5 + e^(k) = 12 / (1/2)
5 + e^k = 24 subtract 5 from both sides
e^k = 19
This implies that
Ln e^k = Ln 19
k * Ln e = Ln 19
k * (1) = Ln 19
k = Ln 19
f(3) = 12 / [ 5 + e^(3 * Ln 19) ] = 1 / 572
Here's the graph : https://www.desmos.com/calculator/9lngaoxfod