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. \[ f(t)=300 e^{0.1 t} \] The product cannot be eaten after the bacteria count reaches $1,800,000$. About how many days will it take before the product is inedible? (Round your answer to the nearest full day.)

Step 1 ：We are given the equation \(f(t)=300 e^{0.1 t}\), where \(t\) represents time in days and \(f(t)\) represents the number of bacteria.

Step 2 ：We are told that the product cannot be eaten after the bacteria count reaches 1,800,000. So we need to solve the equation \(300 e^{0.1 t} = 1800000\) for \(t\).

Step 3 ：To do this, we can take the natural logarithm of both sides to isolate \(t\).

Step 4 ：By solving the equation, we find that \(t\) is approximately 87.

Step 5 ：Final Answer: It will take approximately \(\boxed{87}\) days before the product is inedible.