I need help with part b. Determine how fast is the area of the stain is increasi

Question

I need help with part b.

Determine how fast is the area of the stain is increasing with respect to time elapsed at the point in time when the radius of the stain is 6 mm. Suppose that f(t) gives the internal temperature (in degreeF) of turkey t hours after it is put in an oven to bake. When the turkey is put in the oven, its internal temparature is 60degreeF. Suppose also that f'(t) = 36.57e-0.138t Determine the internal temperature of the turkey after one hour of baking by first finding f(t). Give the temperature accurate to two decimal places Determine the internal temperature of the turkey after three hours of baking without using f(t). Give the temperature accurate to two decimal places.

Explanation / Answer

f'(t) = 36.57*e^(-0.138t)

f(3)-f(1)/(3-1) = integral from 1 to 3 36.57 * e^(-0.138t)

f(3)- f(1) = 2 * 36.57* (e^(-0.138*3) - e^(-0.138*1)/-0.138

f(3) - f(1) = 111.351802454339474

f(3) = 111.351802454339474 + f(1) = 111.35 + 94.16 = 205.51

after three hours temeperature is 205.51 C.

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