Answer:
We have:
f(x) = 14*(5)^x
And we want to write this in the form:
g(x) = A*e^(k*x)
We want to have f(x) = g(x)
This is ratter easy.
The general case is:
A*(r)^x = B*e^(k*x)
Here we have:
A = B
Then:
(r)^x = e^(k*x)
Now we can remember the relation:
(a^x)^y = a^(x*y)
Then we can write:
e^(k*x) = (e^k)^x
Then we have:
(r)^x = (e^k)^x
Then we must have:
r = e^k
Now let's go to our case:
14*(5)^x = A*e^(k*x) = A*(e^k)^x
Then we have:
14 = A
5 = (e^k)
With this equation we can find the value of k.
ln(5) = ln(e^k) = k
ln(5) = k
Then the equation g(x) is:
g(x) = 14*e^(ln(5)*x)
Answer:
A0=14 k +ln9
Step-by-step explanation:
To rewrite the model with the base e, we use the fact that for all b>0,
b=eln(b)
Using this property, and then the power property of logarithms, on 9x, we find that
(9)x=eln(9x)=exln(9)=e(ln(9))x
So we find that
14(9)x=14eln(9)x
So A0=14 and k=ln(9).
