Welcome to Westonci.ca, your go-to destination for finding answers to all your questions. Join our expert community today! Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
Sagot :
The above question is incomplete
Complete Question
Maurice takes a roast out of the oven when the internal temperature of the roast is 165°F. After 10 minutes, the temperature of the roast drops to 145°F.
The temperature of the room is 72°F.
How long does it take for the temperature of the roast to drop to 120°F?
Answer:
27.3143 minutes
Step-by-step explanation:
Using the Newton's law of cooling: The formula is given as:
T (t) = T₀ + T₁ e^ (rt)
Where
T₀ = Original temperature of the room (°F) ; 72°F
T₁ = Temperature of the roast (°F)
This is calculated as:
165 - 72 =93°F
r = Rate of cooling (°F/min)
t = time (min)
Substituting the values, we can obtain:
T (t) = 72 + 93 e ^rt
Step 1
We solve for r
From the question, we know that: the temperature dropped to 145°F after 10 minutes,
t =10 mins and T(10) = 145 °F
Substituting
T(10) = 72 +93 e^10r
145 = 72 + 93 e^10r
145 - 72 = 93 e^10r
Divide both sides by 93
(145-72)/93 = e^(10r)
We take the natural logarithm of both the left and right hand sides
In [(145-72)/93 ] = In (e^10r)
In [(145-72)/93 ] = 10r
-0.24214 =10r
r = -0.24214/10
r = -0.02421 °F/min
Substituting into
-0.02421 °F/min for r in the Equation below
T (t) = 72 + 93 e ^rt
T (t) = 72 + 93 e^ (-0.024214t)
To find the time taken to reach 120°F, we substitute into equation
120 = 72 +93 e^(-0.024214 ×t)
(120-72)= 93 e^ (-0.024214t)
Divide bother sides by 93
[(120-72)/93] = e^-0.024214t
We take the natural logarithm of both sides
In[(120-72)/93] = In(e^-0.024214t)
-0.66139 = -0.024214t
Divide both sides by -0.024214t
t = -0.66139/ -0.024214
t =27.3143 minutes
Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.
