Exercise 18 Page 286

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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