Exercise 75 Page 478

We want to identify the behavior and the growth or decay factor of the given exponential function. Let's first recall the general form of an exponential function.

y= a * b^x
Here, a is the initial amount and the base b is the growth or decay factor.

• When a > 0 and b > 1 the function models exponential growth. The base b represents the growth factor.
• When a > 0 and b < 1 the function models exponential decay. The base b represents the decay factor.

Let's now consider the given function. g(x)= 1.3 * (1/4)^x We see that a= 1.3 and b=14. Since the base of the exponent is less than 1, the function represents exponential decay and its decay factor is 14.