Exponential Growth And Decay Word Problems Worksheets [PDF]: Algebra 2 Math

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.

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:

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.
Convert Growth Rate to Decimal: Convert the percentage growth rate to a decimal. $\newline$ To convert a percentage to a decimal, divide by $100$ . $\newline$ $r = 10\% = \frac{10}{100} = 0.10$
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. $\newline$ $t = 2$
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.
Calculate Future Population: Substitute the known values into the formula and calculate the population after $2$ years. $\newline$ $P(2) = 850,000 \times (1 + 0.10)^2$ $\newline$ $P(2) = 850,000 \times (1.10)^2$ $\newline$ $P(2) = 850,000 \times 1.21$ $\newline$ $P(2) = 1,028,500$
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.