Exercise 17 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 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