Question

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
growth % increase submit answer

Explanation:

Step1: Recall exponential function form

The general form of an exponential function is \( y = a(b)^x \), where \( a \) is the initial amount, and \( b \) is the base. If \( b > 1 \), it's growth; if \( 0 < b < 1 \), it's decay.
Here, the function is \( y = 16(1.059)^x \), so \( b = 1.059 \).

Step2: Determine growth/decay and rate

Since \( 1.059 > 1 \), it's growth. To find the percentage rate, use the formula: percentage rate \( = (b - 1) \times 100\% \).
Calculate \( (1.059 - 1) \times 100\% = 0.059 \times 100\% = 5.9\% \).

Answer:

Growth, 5.9% increase