The differential equation below models the temperature of an 89°C cup of coffee in a 21°C room, where it is known that the coffee cools at a rate of 1°C per minute when its temperature is 71°C. Solve the differential equation to find an expression for the temperature of the coffee at time t. (Let y be the temperature of the cup of coffee in °C, and let t be the time in minutes, with t = 0 corresponding to the time when the temperature was 89°C.) dy/dt = -1/50(y - 21)
Added by Jay K.
Close
Step 1
Step 1:** Divide both sides of the given differential equation by \(y-21\) to isolate the variables: \[\frac{dy}{dt} = -\frac{1}{50}(y-21)\] ** Show more…
Show all steps
Your feedback will help us improve your experience
Darshan Maheshwari and 50 other Calculus 2 / BC educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Supreeta N.
Temperature readings $T$ (in $^{\circ} \mathrm{F}$ ) were recorded every two hours from midnight to 2: 00 PM in Baltimore on September 26,2007 . The time $t$ was measured in hours from midnight. $$\begin{array}{|c|c|c|c|c|c|c|c|c|}\hline t & 0 & 2 & 4 & 6 & 8 & 10 & 12 & 14 \\\hline T & 68 & 65 & 63 & 63 & 65 & 76 & 85 & 91 \\\hline\end{array}$$ (a) Use the readings to sketch a rough graph of $T$ as a function of $t.$ (b) Use your graph to estimate the temperature at 11: 00 AM.
Functions and Models
Four Ways to Represent a Function
Temperature readings T (in $^{\circ} \mathrm{F}$) were recorded every two hours from midnight to $2 : 00 \mathrm{PM}$ in Atlanta on June $4,2013 .$ The time $t$ was measured in hours from midnight. $$\begin{array}{|c|c|c|c|c|c|c|c|c|}\hline t & {0} & {2} & {4} & {6} & {8} & {10} & {12} & {14} \\ \hline T & {74} & {69} & {68} & {66} & {70} & {78} & {82} & {86} \\ \hline\end{array}$$ (a) Use the readings to sketch a rough graph of $T$ as a function of $t .$ (b) Use your graph to estimate the temperature at $9 : 00$ AM.
Functions and Limits
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD