find growth/decay percentage (level 1)\nquestion\ngiven the following exponential function, identify whether…
find growth/decay percentage (level 1)\nquestion\ngiven the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.\n( y = 570(1.01)^x )
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 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