A loaf of bread is taken out of an oven. At t=0, its core temperature is 98 °C. The bakery kitchen is kept at 75 °F. Ten minutes later, the bread’s core temperature is measured to be 70 °C.
a. (i) Convert the ambient temperature to degrees Celsius, correct to one decimal place.
b. (ii) Form the differential equation satisfied by the temperature θ(t) of the bread (in °C) at time t minutes, and solve it to obtain θ(t) in terms of an unknown constant k.
c. (iii) Determine the value of k using the data provided.
d. (iv) Using the value of k found in part (iii), calculate the bread’s temperature after a further 15 minutes.
e. (v) After how many minutes from t=0 will the bread’s core temperature reach 40 °C? (Give your answer correct to two decimal places.)