50000=100*2^(t/3)
Solve for t.
I'm not sure how to solve for t when it's an exponent and a fraction.
Please help because I need the answer to this very soon.
$\displaystyle \Rightarrow 200 = 2^{t/(1/2)} = 2^{2t}$ since $\displaystyle \frac{t}{1/2} = 2t$.
Then $\displaystyle \log_{10} 200 = \log_{10} 2^{2t} = 2t \log_{10} 2 \Rightarrow 2t = \frac{\log_{10} 200 }{\log_{10} 2} \Rightarrow t = \frac{\log_{10} 200 }{2 \log_{10} 2}$.
This answer can also be written as $\displaystyle t = \frac{\log_{10} 200 }{\log_{10} 4}$.
The reason I use base 10 rather than base 2 is so that a scientific calculator can be used to get a decimal approximation of the answer if required.