Answer:
The formula f(t) will be:
[tex]\:f\left(t\right)=2150\left(0.962\right)^t[/tex]
Step-by-step explanation:
We know that exponential decline in Maths can be termed as a consistent reduction of an amount by percentage over a certain period of time.
It can be expressed using the formula
[tex]f\left(t\right)=\:a\:\left(1-b\right)^t[/tex]
here
f(t) represents the final amount
a represents the original amount
b represents the decay factor
t represents the amount that has passed
Now, map our problem using the same concept formula
as
2150 members are at the beginning, so
a = 2150
as the size of the population has been experiencing an annual decline of 3.8%. so
b = 3.8%= 0.038
so substituting b = 0.038 and a = 2150
[tex]P=f\left(t\right)=\:a\:\left(1-b\right)^t[/tex]
[tex]\:f\left(t\right)=2150\left(1-0.038\right)^t[/tex]
[tex]\:f\left(t\right)=2150\left(0.962\right)^t[/tex]
Therefore, the formula f(t) will be:
[tex]\:f\left(t\right)=2150\left(0.962\right)^t[/tex]
