Question

The following equation represents the growth of bacteria in a particular food product, where t represents time in days and f(t) represents the number of bacteria.f(t) = 700e0.1tThe product cannot be eaten after the bacteria count reaches 2,800,000. About how many days will it take before the product is inedible? (Round your answer to the nearest full day.)

Answer 1

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:

`\begin{gathered} 700e^(0.1t)=2800000 \\ e^(0.1t)=(2800000)/(700) \\ e^(0.1t)=4000 \\ \ln e^(0.1t)=\ln4000 \\ 0.1t=\ln4000 \\ t=(1)/(0.1)\ln4000 \\ t=82.9 \\ t\approx83 \end{gathered}`

Therefore, it will take 83 days for the food to be spoiled.