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.

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

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

substitute

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15