QQuestionMathematics
QuestionMathematics
y= 100(1.25)
x
A. Does this function represent exponential growth or exponential decay?
B. What is your initial value?
C. What is the rate of growth or rate of decay?
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Answer
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Step 1:I'll solve this problem step by step, following the specified LaTeX formatting guidelines:
Step 2:: Identify the Exponential Function Form
The given function is in the standard exponential form: $$y = 100(1.25)^{x}
Step 3:: Determine Growth or Decay
- The base of the exponential function is 1.25 - Since 1.25 > 1, this represents exponential growth - When the base is greater than 1, the function increases as x increases A.
Final Answer
Step 3: Identify Initial Value - In the exponential function y = a(b)^{x}, the initial value is the coefficient before the base - Here, the initial value is 100 B. Step 4: Calculate Rate of Growth - The rate of growth is the base minus 1 - Base = 1.25 - Growth rate = 1.25 - 1 = 0.25 or 25% C.
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