Determine Exponential Growth And Decay Worksheet

Algebra 2
Exponential Functions

Total questions - 6

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How Will This Worksheet on "Determine Exponential Growth and Decay" Benefit Your Student's Learning?

  • Helps students grasp how phenomena like population growth, radioactive decay, and interest rates work in real life.
  • Enhances the ability to evaluate and understand exponential changes.
  • Strengthens their hold close of exponential features and the way they practice extraordinary situations.
  • Teaches college students to develop strategies for tackling complicated problems related to exponential growth and decay.
  • Shows how exponential boom and rot are important in numerous subjects, linking science and math collectively.
  • Improves abilities in studying and deciphering facts trends, that's critical for studies and facts technology.

How to Determine Exponential Growth and Decay?

  • Determine if the problem describes exponential growth (increase) or decay (decrease) over time.
  • Note the starting quantity \( a \) given in the problem.
  • Identify the growth rate \( r \) for growth or the decay rate \( r \) for decay, usually given as a percentage or decimal.
  • Apply the exponential growth formula \( y = a \cdot (1 + r)^t \) or the decay formula \( y = a \cdot (1 - r)^t \) to solve for the quantity \( y \) after time \( t \).

Solved Example

Q. How does g(x)=10xg(x) = 10^x change over the interval from x=1x = 1 to x=3x = 3?\newlineChoices:\newlineg(x)g(x) increases by a factor of 2020\newlineg(x)g(x) increases by a factor of 100100\newlineg(x)g(x) decreases by 20%20\%\newlineg(x)g(x) decreases by a factor of 1010
Solution:
  1. Evaluate g(x)g(x) at lower bound: Evaluate g(x)g(x) at the lower bound of the interval.\newlineWe need to find the value of g(x)g(x) when x=1x = 1.\newlineCalculate g(1)=101g(1) = 10^1.
  2. Evaluate g(x)g(x) at upper bound: Evaluate g(x)g(x) at the upper bound of the interval.\newlineWe need to find the value of g(x)g(x) when x=3x = 3.\newlineCalculate g(3)=103g(3) = 10^3.
  3. Determine direction of change: Determine the direction of change in g(x)g(x) over the interval.\newlineCompare g(1)g(1) and g(3)g(3) to see if g(x)g(x) increases or decreases.\newlineSince 10310^3 is greater than 10110^1, g(x)g(x) increases from x=1x = 1 to x=3x = 3.
  4. Calculate growth factor: Calculate the factor by which g(x)g(x) increases over the interval.\newlineDivide g(3)g(3) by g(1)g(1) to find the growth factor.\newlineCalculate the growth factor as: \newline103101=1031=102=100\frac{10^3}{10^1} = 10^{3-1} = 10^2 = 100
  5. Match growth factor with choices: Match the calculated growth factor with the given choices.\newlineThe growth factor is 100100, so g(x)g(x) increases by a factor of 100100 from x=1x = 1 to x=3x = 3.
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About Worksheet

Algebra 2
Exponential Functions

Exponential growth and decay describe changes over time. For growth, the quantity increases by a fixed percentage, modeled as \( y = a \cdot (1 + r)^t \); the growth factor is \( 1 + r \). For decay, the quantity decreases similarly, modeled as \( y = a \cdot (1 - r)^t \). Determine growth or decay by checking if \( r \) is positive or negative. Use these worksheets to enhance your problem solving skills.

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