Answer:
-Exponential Decay
-Decay factor is (1-0.05)
Step-by-step explanation:
-Given that the number decreases by a defined rate each year from the initial size by 5%,
-This is an exponential decay function of the form:
[tex]y=Ae^{-rt}[/tex]
Where:
[tex]y[/tex] is the quantity/size after time t
[tex]A[/tex] is the initial size
[tex]r[/tex] is the rate of decay
-Our function can the be written as
[tex]y=45000e^{-0.05t}[/tex]
Hence, the decay rate/factor is 0.05
#Alternatively
The exponential decay can be of the form:
[tex]y=ab^x[/tex]
Where:
y is the size at time x, a is the initial size, x is time and b is the decay factor.
b is of the form [tex]b=(1-r),\ \ r=decay\ rate[/tex]
[tex]y=ab^x\\\\y=45000(1-0.05)^x[/tex]
Hence, the decay factor is (1-0.05)
