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QA
At time t = 0, a boiled potato is taken from a pot on a stove and left to cool in a kitchen. The internal
temperature of the potato is 91 degrees Celsius (°C) at time t = 0, and the internal temperature of the potato
is greater than 27°C for all times t > 0. The internal temperature of the potato at time t minutes can be
modeled by the function H that satisfies the differential equation
dH
(H-
(H-27), where H(t) is
dt
measured in degrees Celsius and H(0) = 91.
(a) Write an equation for the line tangent to the graph of Hat t = 0. Use this equation to approximate the
internal temperature of the potato at time t = 3.
(b) Use
2017 APⓇ CALCULUS AB FREE-RESPONSE QUESTIONS
(a) dH
d²H
dt²
to determine whether your answer in part (a) is an underestimate or an overestimate of the
internal temperature of the potato at time t = 3.
(c) For t < 10, an alternate model for the internal temperature of the potato at time 7 minutes is the function
-= − (G - 27)²/3, where G(t) is measured in degrees Celsius
dG
G that satisfies the differential equation
dt
and G(0) = 91. Find an expression for G(t). Based on this model, what is the internal temperature of the
potato at time t = 3 ?
564
at (21-27)
-
==
2-16
To = - = (H(3)-27)
4
-64 = HB)-27
-37 = H (3)
(b) _d²fi
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