To write an exponential function to model the given situation, let's first recall the general form of an exponential equation.
y=a b^x
In this formula a is the initial value and b= 1+r, where r is the rate of change. If the function represents growth, then r>0. If it represents decay, then r<0.
Writing the Equation
To write the function, we first need to define the variables. Let y be the population and let x be the number of years after the initial value. In this case, the initial value is a population of 100 000. Since the population decreases 2 % each year, we have that r=- 0.02.
y=100 000 [ 1+(- 0.02)]^x
⇕
y=100 000 ( 0.98)^x
