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.

Answer 1

Answer:

D(t)=50(0.8)^t

Step-by-step explanation:

Answer 2

Answer:

$D(t)=50^o(0.80)^t$

Step-by-step explanation:

The correct question is

At the moment a hot cake is put in a cooler, the difference between the cake's and the cooler's temperatures is 50 degree 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

we know that

The equation of a exponential decay function is equal to

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

where

D(t) is the temperature difference in degrees

t is the number of minutes

r is the rate of change

a is the initial value

we have

$a=50^oC$

$r=\frac{1}{5}=0.20$

substitute

$D(t)=50^o(1-0.20)^t$

$D(t)=50^o(0.80)^t$