MHB Finding Temperature of Hot Sandwich: Equation & Answers

  • Thread starter Thread starter arroww
  • Start date Start date
  • Tags Tags
    Temperature
AI Thread Summary
The discussion revolves around calculating the temperature of a hot sandwich using the equation T(t) = 63(0.5)^(t/10) + 19. To find the initial temperature when recording begins, substitute t = 0 into the equation, resulting in T(0) = 63 + 19 = 82 degrees Celsius. For part b, substituting t = 20 into the equation gives T(20) = 63(0.5)^(2) + 19, which simplifies to approximately 54.75 degrees Celsius. Participants seek clarification on how to properly substitute values into the equation to find the temperatures. Understanding the substitution process is crucial for solving similar problems.
arroww
Messages
16
Reaction score
0
9) A student records the internal temperature of a hot sandwich that has been left to cool on a kitchen counter. The room temperature is 19 degrees Celsius. An equation that models this situation is $$T(t) = 63(0.5)^\frac{t}{10} + 19$$ where $$T$$ is the temperature in degrees Celsius and $$t$$ is the time in minutes.

a) What was the temperature of the sandwich when she began to record its temperature?
b) Determine the temperature of the sandwich after 20 min.I don't really understand what to do..help would be appreciated. Thanks!
 
Mathematics news on Phys.org
The equation you are given tells you the temperature of the sandwich at time $t$. So, you need to substitute for $t$ and then evaluate the resulting expression on the right side of the equation. What is the value of $t$ for part a)? And for part b)?
 

Thread 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
View full post »
Thread 'Imaginary Pythagoras'

Thread 'Imaginary Pythagoras'

I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...
View full post »

Thread 'Fermat's Last Theorem'

Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
View full post »

Similar threads

MHB Is my answer correct? (Exponential Functions)
Replies
1
Views
1K
MHB Sammy's question at Yahoo Answers regarding Newton's Law of Cooling
Replies
1
Views
2K
Answer: Terminal Temperature of Water with Ice Cube
Replies
6
Views
3K
MHB 3.1.5 AP Calculus Exam average temperature
Replies
3
Views
2K
What was the temperature of the object?
Replies
4
Views
2K
Find the temperature of Liquid A after 12 minutes
Replies
13
Views
2K
How Hot Was the Campfire's Aluminum Can Before Cooling in Water?
Replies
2
Views
2K
Hot Air Balloon: Find inside temperature given size, load
Replies
10
Views
7K
Heat required to increase the temperature
Replies
4
Views
2K
MHB Differential Equations of Calculus Problems- Calc I course
Replies
4
Views
3K

Hot Threads

Recent Insights

Back
Top