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 weight of the catfish and x be the number of weeks after the initial value. In this case, the initial value is a weight of 0.1. Since the weight increases by about 23 % each week, we have that r= 0.23.
y=0.1 (1+0.23)^x
⇕
y=0.1( 1.23)^x
b Since we want to find the weight of the catfish after 4 weeks, we will substitute 4 for x in our model equation.
