Answer:
[Tex]D(t)=50\cdot (0.8)^{t}[/Tex]
Step-by-step explanation:
The equation for exponential decay function is given as:
[Tex]D(t)=a(1-r)^{t}[/Tex]
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=[Tex]\frac{1}{5}[/Tex]
Therefore the function for the difference in temperature is given as:
[Tex]D(t)=50(1-\frac{1}{5})^{t}[/Tex]
[Tex]D(t)=50\cdot (\frac{4}{5})^{t}[/Tex]
We can convert [Tex]\frac{4}{5}[/Tex] to decimal and write the function as:
[Tex]D(t)=50\cdot (0.8)^{t}[/Tex]
