SOLUTION: Assume that the number of viruses present in a sample is modeled by the exponential function "f(t) = 10t", where t is the elapsed time in minutes. How would you apply logarithms to

Algebra ->  Inequalities -> SOLUTION: Assume that the number of viruses present in a sample is modeled by the exponential function "f(t) = 10t", where t is the elapsed time in minutes. How would you apply logarithms to      Log On


   



Question 27166: Assume that the number of viruses present in a sample is modeled by the exponential function "f(t) = 10t", where t is the elapsed time in minutes. How would you apply logarithms to determine when the sample will grow to 5 billion viruses?
~I am not sure how to answer this question...can someone please help me?! Thank you!~

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Your equation is
f%28t%29+=+10%5Et
You want to know when f(t) = 5 billion
or
f%28t%29+=+5%2A10%5E9 in scientific notation
so
5%2A10%5E9+=+10%5Et
Take the log of both sides
log%285%2A10%5E9%29+=+log%2810%5Et%29
use the rules
log(a*b*c* ... ) = log(a) + log(b) + log(c) + ...
and
log(10^k) = k
log%285%2A10%5E9%29+=+log%2810%5Et%29
log%285%29+%2B+log%2810%5E9%29+=+log%2810%5Et%29
log%285%29+%2B+9+=+t