Question

given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
$y = 10(1.01)^x$

Explanation:

Step1: Compare to standard exponential form

The standard exponential function is $y = a(1+r)^x$, where $a$ is the initial value, $r$ is the rate of growth/decay, and $x$ is the independent variable. For growth, $1+r>1$; for decay, $0<1+r<1$.
Given $y = 10(1.01)^x$, here $1+r = 1.01$.

Step2: Identify growth/decay

Since $1.01>1$, this is exponential growth.

Step3: Calculate percentage rate

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

Answer:

Growth, 1% increase