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

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.

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) = 10^x

change over the interval from

x = 1

x = 3

\newline

Choices:

\newline

g(x)

increases by a factor of

20

\newline

g(x)

increases by a factor of

100

\newline

g(x)

decreases by

20\%

\newline

g(x)

decreases by a factor of

10

Solution:

Evaluate $g(x)$ at lower bound: Evaluate $g(x)$ at the lower bound of the interval. $\newline$ We need to find the value of $g(x)$ when $x = 1$ . $\newline$ Calculate $g(1) = 10^1$ .
Evaluate $g(x)$ at upper bound: Evaluate $g(x)$ at the upper bound of the interval. $\newline$ We need to find the value of $g(x)$ when $x = 3$ . $\newline$ Calculate $g(3) = 10^3$ .
Determine direction of change: Determine the direction of change in $g(x)$ over the interval. $\newline$ Compare $g(1)$ and $g(3)$ to see if $g(x)$ increases or decreases. $\newline$ Since $10^3$ is greater than $10^1$ , $g(x)$ increases from $x = 1$ to $x = 3$ .
Calculate growth factor: Calculate the factor by which $g(x)$ increases over the interval. $\newline$ Divide $g(3)$ by $g(1)$ to find the growth factor. $\newline$ Calculate the growth factor as: $\newline$ $\frac{10^3}{10^1} = 10^{3-1} = 10^2 = 100$
Match growth factor with choices: Match the calculated growth factor with the given choices. $\newline$ The growth factor is $100$ , so $g(x)$ increases by a factor of $100$ from $x = 1$ to $x = 3$ .