Question

Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
y, equals, 990, left parenthesis, 1, point, 9, 2, 2, right parenthesis, to the power x
y=990(1.922)
x

Answer 1

To identify whether the change represented by the given exponential function is growth or decay, we can look at the base of the exponential function. The function you provided is:

\[ y = 990(1.922)^x \]

In this function, the base \(1.922\) is greater than \(1\). When the base of an exponential function is greater than \(1\), it indicates that the function is experiencing exponential growth. Conversely, if the base were between \(0\) and \(1\), it would indicate exponential decay.

Next, to determine the percentage rate of increase, we can use the formula for percentage change, which is given by:

\[
\text{Percentage rate of increase} = (b - 1) \times 100\%
\]

Here \(b\) represents the base of the exponential function, which in this case is \(1.922\). Therefore:

\[
\text{Percentage rate of increase} = (1.922 - 1) \times 100\% = 0.922 \times 100\% = 92.2\%
\]

In summary, the change represented by the function is exponential growth, and the percentage rate of increase is \(92.2\%\).