Question

In: Advanced Math

Write a formula that models this situation. For the following exercises, use this scenario: A turkey is taken out of the oven with an internal temperature of 165° Fahrenheit..

For the following exercises, use this scenario: A turkey is taken out of the oven with an internal temperature of 165° Fahrenheit and is allowed to cool in a 75° F room. After half an hour, the internal temperature of the turkey is 145° F.

Write a formula that models this situation.

Expert Solution

Consider that a turkey is taken out of the oven with an internal temperature of 165°F and allowed to cool in a 75°F room. After 30 minutes the internal temperature of the turkey was145°F.

Suppose that internal temperature of the turkey after t minutes is

T(t) = Aekt + 75

Since,

T(0) = 165

So,

165 = Aek(0) + 75

165 – 75 = A

A = 90

Since T(30) = 145

So,

145 = 90ek(30) + 75

70 = 90ek(30)

ek(30) = 70/90

k = 1/30 ln(7/9)

k = -0.0084

Hence, the internal temperature of the soup after t minutes is T(t) = 90e-0.0084t + 75.

Junaid answered 1 year ago

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