To determine after how many days the food is not edible we need to equate the expression to the number of bacteria when it stops being edible and we solve the equation:
[tex]\begin{gathered} 700e^{0.1t}=2800000 \\ e^{0.1t}=\frac{2800000}{700} \\ e^{0.1t}=4000 \\ \ln e^{0.1t}=\ln4000 \\ 0.1t=\ln4000 \\ t=\frac{1}{0.1}\ln4000 \\ t=82.9 \\ t\approx83 \end{gathered}[/tex]
Therefore, it will take 83 days for the food to be spoiled.
