An object with initial temperature is placed in an oven at time

MATHEMATICS · Single correct · AP · Calculus AB · Differential Equations · Differential Equations

Problem

An object with initial temperature 20∘ ⁣C20^{\circ}\!\text{C} is placed in an oven at time t=0t=0. For the first 55 minutes its temperature T(t)T(t) satisfies dTdt=0.1T\dfrac{dT}{dt}=0.1T. After t=5t=5 minutes the oven is turned off, and for t≥5t\ge5 the object cools so that dTdt=−0.05T\dfrac{dT}{dt}=-0.05T. What is T(8)T(8), the temperature in degrees Celsius after 88 minutes? (a) Approximately 44.544.5 (b) Approximately 24.424.4 (c) Approximately 28.428.4 (d) Approximately 38.338.3

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