# Exponential Growth And Decay Word Problems Worksheet

## 6 problems

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.

Algebra 2
Exponential Functions

## 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 $850,000$ people, which increases by $10\%$ every year due to a growing tech industry. What will the population be in $2$ 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 $P_0$ is $850,000$ people, and the growth rate $r$ is $10\%$ per year.
2. Convert Growth Rate to Decimal: Convert the percentage growth rate to a decimal.$\newline$To convert a percentage to a decimal, divide by $100$.$\newline$$r = 10\% = \frac{10}{100} = 0.10$
3. Determine Number of Years: Determine the number of years ($t$) over which the population grows.$\newline$The population is growing over a period of $2$ years.$\newline$$t = 2$
4. Use Exponential Growth Formula: Use the formula for exponential growth to calculate the future population. The formula for exponential growth is $P(t) = P_0 \times (1 + r)^t$, where $P(t)$ is the population at time $t$, $P_0$ is the initial population, $r$ is the growth rate, and $t$ is the time in years.
5. Calculate Future Population: Substitute the known values into the formula and calculate the population after $2$ years.$\newline$$P(2) = 850,000 \times (1 + 0.10)^2$$\newline$$P(2) = 850,000 \times (1.10)^2$$\newline$$P(2) = 850,000 \times 1.21$$\newline$$P(2) = 1,028,500$
6. Round Answer if Necessary: Round the answer to the nearest whole number if necessary.$\newline$The calculated population is already a whole number, so no rounding is necessary.

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