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 number of members in 2010, and let x be the number of years after the initial value. In this case the initial value is the initial number of members, which is 500 000. Since the number of members increases 15 % each year, we have that r= 0.15.
y=500 000 (1+0.15)^x
⇕
y=500 000 ( 1.15)^x
b Since we want to find the number of members in 2016 — which is 6 years after 2010 — we will substitute 6 for x in our model equation.
