given the following exponential function, identify whether the change represents growth or decay, and…

Explanation:

Step1: Recall exponential function form

The general form of an exponential function is ( y = a(b)^x ), where ( a ) is the initial amount, and ( b ) is the base. If ( b>1 ), it's growth; if ( 0 < b < 1 ), it's decay. The growth/decay rate ( r ) is related to ( b ) by ( b=1 + r ) (for growth) or ( b = 1 - r ) (for decay).

Step2: Analyze the given function

For the function ( y = 30(1.003)^x ), the base ( b = 1.003 ). Since ( 1.003>1 ), this represents growth.

Step3: Calculate the growth rate

Using the formula ( b = 1 + r ), we substitute ( b = 1.003 ): ( 1.003=1 + r ) Subtract 1 from both sides: ( r=1.003 - 1=0.003 ) To convert this to a percentage, multiply by 100: ( r = 0.003\times100 = 0.3% )

Answer:

The change represents growth with a percentage rate of increase of ( 0.3% ).