Exponential and logarithmic models

Question

A roasted Turkey is taken from an oven when its temperature has reached 185 degrees Fahrenheit and is placed on a table in a room where the temperature is 75 degrees Fahrenheit. Give answers accurate to at least 2 decimal places.

a) if the temperature of the Turkey is 143 degrees Fahrenheit after half an hour, what is its temperature after 45 minutes?

________ Fahrenheit

b) when will the Turkey cool to 100 degrees Fahrenheit?

________ hours

Answer 1

The exponential model is y = a(r)^x, where a is the starting temperature, r is the rate of growth/decay or increase/decrease, and x = time in minutes. We do not yet know the rate at which the temperature is decreasing, but we can solve and find out.

143 = 183(r)³⁰ (you could also use 0.5 if time is in hours)

Solve the equation for r, then you will have a formula y = a(r)^x where you know 'a' and 'r'. Now use it to find the temp after 45 minutes. For part b, substitute y with 100 and solve for x to find out how long.