At the moment a hot cake is put in a cooler, the difference between the cake's and the cooler's temperatures is 50^(@) Celsius. This causes the cake to cool and the temperature difference loses (1)/(5) of its value every minute. Write a function that gives the temperature difference in degrees Celsius, D(t),t minutes after the cake was put in the cooler. D(t)= ◻

Initial Temperature Difference: The initial temperature difference is 50 degrees Celsius, so D(0) = 50.Decay Rate Calculation: The temperature difference decreases by (1)/(5) of its current value each minute, so the decay factor is 1 - (1)/(5) = (4)/(5) per minute.Exponential Decay Function: The function for the temperature difference is an exponential decay function, D(t) = D(0) * (decay factor)^(t).Substitution into Equation: Substitute D(0) = 50 and decay factor = (4)/(5) into the equation: D(t) = 50 * ((4)/(5))^(t).

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

At the moment a hot cake is put in a cooler, the difference between the cake's and the cooler's temperatures is
50^(@) Celsius. This causes the cake to cool and the temperature difference loses
(1)/(5) of its value every minute.
Write a function that gives the temperature difference in degrees Celsius,
D(t),t minutes after the cake was put in the cooler.

D(t)=

◻

At the moment a hot cake is put in a cooler, the difference between the cake's and the cooler's temperatures is $50^{\circ}$ Celsius. This causes the cake to cool and the temperature difference loses $\frac{1}{5}$ of its value every minute. $\newline$ Write a function that gives the temperature difference in degrees Celsius, $D(t), t$ minutes after the cake was put in the cooler. $\newline$ $D(t)=$ $\square$

View step-by-step help

Home

Math Problems

Algebra 2

Write equations of cosine functions using properties

Full solution

Q. At the moment a hot cake is put in a cooler, the difference between the cake's and the cooler's temperatures is

50^{\circ}

Celsius. This causes the cake to cool and the temperature difference loses

\frac{1}{5}

of its value every minute.

\newline

Write a function that gives the temperature difference in degrees Celsius,

D(t), t

minutes after the cake was put in the cooler.

\newline

D(t)=

\square

Initial Temperature Difference: The initial temperature difference is $50$ degrees Celsius, so $D(0) = 50$ .
Decay Rate Calculation: The temperature difference decreases by $(1)/(5)$ of its current value each minute, so the decay factor is $1 - (1)/(5) = (4)/(5)$ per minute.
Exponential Decay Function: The function for the temperature difference is an exponential decay function, $D(t) = D(0) \cdot (\text{decay factor})^{t}$ .
Substitution into Equation: Substitute $D(0) = 50$ and decay factor $= \frac{4}{5}$ into the equation: $D(t) = 50 \times \left(\frac{4}{5}\right)^{t}$ .