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 equation we first need to define the variables. Let y be the population in 2000, and let x be the number of years after the initial value. In this case, the initial value is a population of 315 000. Since the population increases 2 % annually, we have that r= 0.02.
y=315 000 (1+0.02)^x
⇕
y=315 000 ( 1.02)^x
b Since we want to find what number of people will be in the city in 2020 — which is 20 years after 2000 — we will substitute 20 for x in our model equation.
