given the following exponential function, identify whether the change represents growth or decay, and…

given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease. \\( y = 16(1.059)^x \\)

given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease. \\( y = 16(1.059)^x \\)

Answer

Explanation:

Step1: Identify growth/decay factor

The exponential function is in the form $y = a(1+r)^x$, where $1+r$ is the base. Here, the base is $1.059$, which is greater than 1, so it is growth.

Step2: Calculate growth rate

Subtract 1 from the base to find the rate: $r = 1.059 - 1$ $r = 0.059$ Convert to percentage: $0.059 \times 100 = 5.9%$

Answer:

Growth, 5.9% increase