Question

At the moment a hot cake is put in a cooler, the difference between the cake's and the cooler's temperatures is 50\degree50°50, degree Celsius. This causes the cake to cool and the temperature difference loses \dfrac15
5

1

​

start fraction, 1, divided by, 5, end fraction of its value every minute.

Write a function that gives the temperature difference in degrees Celsius, D(t)D(t)D, left parenthesis, t, right parenthesis, ttt minutes after the cake was put in the cooler.

D(t)=D(t)=D, left parenthesis, t, right parenthesis, equals

Answer 1

Answer:

$D(t)=50\cdot (0.8)^{t}$

Step-by-step explanation:

The equation for exponential decay function is given as:

$D(t)=a(1-r)^{t}$

where:

D(t)= difference in temperature t=time

r=rate of change

a =initial value of the temperature

From the given problem:

Initial Temperature,a=50°C

Rate of Decay,r=$\frac{1}{5}$

Therefore the function for the difference in temperature is given as:

$D(t)=50(1-\frac{1}{5})^{t}$

$D(t)=50\cdot (\frac{4}{5})^{t}$

We can convert $\frac{4}{5}$ to decimal and write the function as:

$D(t)=50\cdot (0.8)^{t}$

Answer 2

Answer:

D(t)=50(0.8)^t

Step-by-step explanation: