Question

given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.

$y = 970(1.042)^x$

Explanation:

Step1: Identify growth/decay

The exponential function is in the form $y = a(1+r)^x$, where $a>0$. If $1+r>1$, it is growth. Here, $1.042>1$, so it is growth.

Step2: Calculate growth rate

Subtract 1 from the base:
$r = 1.042 - 1$
$r = 0.042$
Convert to percentage: $0.042 \times 100 = 4.2$

Answer:

Growth, 4.2% increase