Question

1. An employee takes a pizza out of a 220°C oven and puts it on the table for pick up. The pizza starts to

cool down 50% every 10 minutes, but stays above the room temperature of 20°C.

a) Write an equation that models the temperature of the pizza immediately after it is taken out of the
oven. (Hint: There is a horizontal asymptote at 20°C)

b) What is the temperature of the pizza, rounded to the nearest degree, when the customer picks it up 15
minutes after it was taken out of the oven?

c) How much time should the customer wait, after they picked up the pizza, before eating it at a safe
temperature of 45°C?

Answer 1

`1a. \: = 20 + 200.( (1)/(2))^{ (t)/(10) }`

`1b. \: = 91^(o) c`

`1c. \: = 30 \: minutes`

Explanation:

`1a. \: t = a + b. {c}^(t)\\ a = 20`

`t(0) = a + b = 220 = > b = 200 \\ c = ((1)/(2))^{ (1)/(10) }`

`t = 20 + 200.( (1)/(2) )^{ (t)/(10) }`

`1b.when \: t = 15 \\ t = 20 + 200.( (1)/(2))^{ (15)/(10) } \\ = 20 + 71 \\ = 91^(o)c`

`1c.when \: t \: = 45 \\ 20 + 200. ((1)/(2) )^{ (t)/(10) \: } = 45 \\200.( (1)/(2))^{ (t)/(10) } = 25 \\ ( (1)/(2) )^{ (t)/(10) } = (1)/(8) \\ (t)/(10) = 3`

`t = 30`