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After cooking a large batch of chili, James puts it immediately in the fridge. The temperature T, in ∘C, t hours after it is placed in the fridge is given by T(t)=90e−5t/M+2, where M is the mass in kilograms of the chili.
Write down
the initial temperature of the chili;
the temperature of the fridge.
Consider the equation T(t)=k.
Show that time taken for the chili to reach a temperature of k°C is given by t=−5M​ln(90k−2​).
Food safety rules dictate that food should not sit in the "danger zone" of 4°Cto56∘C for more than two hours.
James calculates that the time his batch of chili will spend in the danger zone is aM, where a∈R.
Using the result from (b), find the value of a.
Hence, determine the largest batch of chili James can safely store in his fridge.
Suggest one way James could store a larger batch safely.
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