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

D(t)= 50(4/5)^t

Explanation:

Answer 2

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

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=(1)/(5)=0.20`

substitute

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

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