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, and 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 210 000. Since the population increases 12.5 % each year, we have that r=0.125.
y=210 000 [ 1+0.125]^x
⇕
y=210 000 ( 1.125)^x
