Science:Math Exam Resources/Courses/MATH102/December 2013/Question B 07/Statement

Initially, a patient has $1000$ copies of the HIV virus. If the smallest detectable viral load is $350,000$ virus particles, how long (in days) will it take until the HIV infection is detectable? Assume that the number of virus particles y grows according to the equation

${\frac {dy}{dt}}=0.05y$

where t is time in days. Leave your answer in terms of logarithms.