Exponential Growth And Decay Word Problems Worksheet

Algebra 2
Exponential Functions

Total questions - 6

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

  • Helps students recognize such things as how populations grow, how radioactive materials decay, and how interest rates affect savings.
  • Teaches students to predict future events based on current trends, essential for planning and decision-making.
  • Makes it simpler for college kids to peer and apprehend how things trade in different conditions where things grow or shrink quickly.
  • Helps college students apprehend how to use math to resolve actual troubles, like figuring out how a lot of money could be stored over time or how rapidly a populace will grow.
  • Encourages college students to provide you with ways to remedy difficult problems in which things are developing or shrinking rapidly.

How to Exponential Growth and Decay Word Problems?

  • Determine whether the problem describes exponential growth (increasing) or decay (decreasing) over time to choose the correct model.
  • Note the initial amount (\(a\)) and the rate (\(r\)), which is often provided as a percentage or decimal.
  • Use \( y = a \cdot (1 + r)^t \) for growth or \( y = a \cdot (1 - r)^t \) for decay, where \(t\) is the time period.
  • Calculate the final amount (\(y\)) and interpret the result within the context of the problem, ensuring it makes logical sense.

Solved Example

Q. Richmond County has a population of 850,000850,000 people, which increases by 10%10\% every year due to a growing tech industry. What will the population be in 22 years? If necessary, round your answer to the nearest whole number.\newline____ people\newline
Solution:
  1. Identify Population and Growth Rate: Identify the initial population and the rate of growth. The initial population P0P_0 is 850,000850,000 people, and the growth rate rr is 10%10\% per year.
  2. Convert Growth Rate to Decimal: Convert the percentage growth rate to a decimal.\newlineTo convert a percentage to a decimal, divide by 100100.\newliner=10%=10100=0.10r = 10\% = \frac{10}{100} = 0.10
  3. Determine Number of Years: Determine the number of years (tt) over which the population grows.\newlineThe population is growing over a period of 22 years.\newlinet=2t = 2
  4. Use Exponential Growth Formula: Use the formula for exponential growth to calculate the future population. The formula for exponential growth is P(t)=P0×(1+r)tP(t) = P_0 \times (1 + r)^t, where P(t)P(t) is the population at time tt, P0P_0 is the initial population, rr is the growth rate, and tt is the time in years.
  5. Calculate Future Population: Substitute the known values into the formula and calculate the population after 22 years.\newlineP(2)=850,000×(1+0.10)2P(2) = 850,000 \times (1 + 0.10)^2\newlineP(2)=850,000×(1.10)2P(2) = 850,000 \times (1.10)^2\newlineP(2)=850,000×1.21P(2) = 850,000 \times 1.21\newlineP(2)=1,028,500P(2) = 1,028,500
  6. Round Answer if Necessary: Round the answer to the nearest whole number if necessary.\newlineThe calculated population is already a whole number, so no rounding is necessary.
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About Worksheet

Algebra 2
Exponential Functions

Exponential growth and decay word problems involve scenarios where quantities change exponentially over time, such as population increases or radioactive decay. Solving these problems requires understanding the mathematical models \( y = a \cdot (1 + r)^t \) for growth and \( y = a \cdot (1 - r)^t \) for decay. Practice with an exponential growth and decay word problems worksheet to master these concepts.

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