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 = 96(1.03)^x )

answer attempt 1 out of 3

growth

% increase

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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 \( y = 96(1.03)^x \). Comparing with \( y = a(1 + r)^x \), we have \( 1 + r = 1.03 \).

Step3: Solve for growth rate \( r \)

Subtract 1 from both sides: \( r = 1.03 - 1 = 0.03 \).

Step4: Convert to percentage

To find the percentage growth rate, multiply \( r \) by 100: \( 0.03\times100 = 3\% \). Also, since \( 1.03>1 \), the function represents growth.

Answer:

The function represents growth with a 3% increase.