Question

find growth/decay percentage (level 1)
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: 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 growth rate (as a decimal), and \( x \) is the time variable.

Step2: Compare with Given Function

The given function is \( y = 570(1.01)^x \). Comparing with \( y = a(1 + r)^x \), we have \( 1 + r = 1.01 \).

Step3: Solve for \( r \)

To find \( r \), subtract 1 from both sides: \( r = 1.01 - 1 = 0.01 \).

Step4: Convert \( r \) to Percentage

To convert the decimal \( r = 0.01 \) to a percentage, multiply by 100: \( 0.01 \times 100 = 1\% \). Also, since \( 1 + r>1 \), this represents growth.

Answer:

Growth, 1% increase