At time t = 0, a bottle of juice is at 84°F is stood in a mountain stream whose temperature is 50°F. After 5 minutes, its temperature is 75°F. Let H(t) denote the temperature of the juice at time t, in minutes. (a) Write a differential equation for H(t) using Newton's Law of Cooling. Use k as the unknown constant. dH (Н -50) k dt (b) Solve the differential equation. NOTE: Round constants to 5 decimal places if needed. H(t) = (c) When will the temperature of the juice have dropped to 56°F? NOTE: Round your answer to the nearest minute. After minutes, the temperature will have dropped to 56°F.

At time t = 0, a bottle of juice is at 84°F is stood in a mountain stream whose temperature is 50°F. After 5 minutes, its temperature is 75°F. Let H(t) denote the temperature of the juice at time t, in minutes. (a) Write a differential equation for H(t) using Newton's Law of Cooling. Use k as the unknown constant. dH (Н -50) k dt (b) Solve the differential equation. NOTE: Round constants to 5 decimal places if needed. H(t) = (c) When will the temperature of the juice have dropped to 56°F? NOTE: Round your answer to the nearest minute. After minutes, the temperature will have dropped to 56°F.

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Description: At time t = 0, a bottle of juice is at 84°F is stood in a mountainstream whose temperature is 50°F. After 5 minutes, its temperatureis 75°F. Let H(t) denote the temperature of the juice at time t, inminutes.(a) Write a differential equation for H(t)

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Question

At time t = 0, a bottle of juice is at 84°F is stood in a mountain
stream whose temperature is 50°F. After 5 minutes, its temperature
is 75°F. Let H(t) denote the temperature of the juice at time t, in
minutes.
(a) Write a differential equation for H(t) using Newton's Law of
Cooling. Use k as the unknown constant.
dH
(Н -50) k
dt
(b) Solve the differential equation.
NOTE: Round constants to 5 decimal places if needed.
H(t) =
(c) When will the temperature of the juice have dropped to 56°F?
NOTE: Round your answer to the nearest minute.
After
minutes, the temperature will have dropped to
56°F.

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