Question

question given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease. \\( y = 220(1.09)^x \\) answer attempt 1 out of 3 growth \\(\\%\\) increase submit answer

Explanation:

Step1: Recall exponential growth formula

The general form of an exponential growth function is \( y = a(1 + r)^x \), where \( a \) is the initial amount, \( r \) is the rate of growth (as a decimal), and \( x \) is the time variable.

Step2: Compare with given function

The given function is \( y = 220(1.09)^x \). Comparing it to \( y = a(1 + r)^x \), we have \( 1 + r = 1.09 \).

Step3: Solve for growth rate \( r \)

Subtract 1 from both sides: \( r = 1.09 - 1 = 0.09 \). To convert this to a percentage, multiply by 100: \( 0.09\times100 = 9\% \). Since \( 1 + r>1 \), it represents growth.

Answer:

The change represents growth with a 9% increase.