Question

given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.\\(y = 570(1.01)^{x}\\)

Explanation:

Step1: Compare to growth/decay form

The standard exponential form is $y = a(1+r)^x$ (growth) or $y = a(1-r)^x$ (decay), where $a>0$. For the given $y=570(1.01)^x$, the base is $1.01>1$, so it is growth.

Step2: Calculate growth rate

Set $1+r = 1.01$. Solve for $r$:
$r = 1.01 - 1 = 0.01$
Convert to percentage: $0.01 \times 100\% = 1\%$

Answer:

This represents exponential growth with a 1% rate of increase.