# Fractional Exponents, functions

• Sep 16th 2008, 03:34 PM
rafaeli
Fractional Exponents, functions
A bacteria culture starts with 500 bacteria and doubles in size every 30 minutes. Graph the population function and estimate the time for the population to reach 20,000.

So far I did 20,000/500 = 2^(x/30)
which is 40= 2^(x/30)
now how do i get rid of the fractional exponent (x/30)??
-----------------------------
Also if g(x) = 4 + x + e^x
find g^-1 (5)
• Sep 16th 2008, 03:50 PM
Jameson
Quote:

Originally Posted by rafaeli
A bacteria culture starts with 500 bacteria and doubles in size every 30 minutes. Graph the population function and estimate the time for the population to reach 20,000.

So far I did 20,000/500 = 2^(x/30)
which is 40= 2^(x/30)
now how do i get rid of the fractional exponent (x/30)??
-----------------------------
Also if g(x) = 4 + x + e^x
find g^-1 (5)

Are you familiar with logarithms? Starting with $40=2^{\frac{x}{30}}$, now take the natural log of both sides and you get $\ln(40)=\ln{ \left( 2^{\frac{x}{30}} \right)}$

Now to get rid of that exponent, use a rule that says $\ln(a^n)=n\ln(a)$ Thus $\ln(40)=\frac{x}{30} \ln(2)$.

Are you with me so far?
• Sep 16th 2008, 05:02 PM
rafaeli
Thank you. I got that part. Took me a while to understand it but I finally got it.
Now i want to know like how many bacteria are there after t hours?