Write Exponential Functions For Word Problems Worksheets [PDF]: Algebra 2 Math

How Will This Worksheet on "Write Exponential Functions for Word Problems" Benefit Your Student's Learning?

Translating word problems into exponential functions helps students practice breaking down complex scenarios into solvable equations.
Writing exponential functions deepens comprehension of exponential growth and decay, reinforcing theoretical knowledge.
This process encourages critical and analytical thinking, prompting students to assess all details to construct accurate functions.
Successfully translating word problems into mathematical functions builds confidence in handling complex math tasks.
Writing accurate exponential functions requires attention to detail and precision, promoting meticulous work habits.
Students improve their ability to read and interpret mathematical language and word problems, valuable across all math areas.

Determine the starting amount or initial condition described in the problem, often denoted as $ a $ in the function $ f(x) = a \cdot b^x $.
Find the rate at which the quantity grows or decays. If the quantity increases, $ b > 1 $; if it decreases, $ 0 < b < 1 $.
Use the identified initial value and growth/decay factor to write the function in the form $ f(x) = a \cdot b^x $, where $ x $ represents time or another variable.
Apply the specific details from the word problem to the function, ensuring all conditions and rates are accurately reflected in the equation.

Solved Example

Q. The town of Valley View conducted a census this year, which showed that it has a population of

1,800

people. Based on the census data, it is estimated that the population of Valley View will grow by

12\%

each decade.

\newline

Write an exponential equation in the form

y=a(b)^x

that can model the town population

, y, x

decades after this census was taken. Use whole numbers, decimals, or simplified fractions for the values of

a

and

b

Solution:

Convert to decimal: Convert $12\%$ to a decimal. $\newline$ $12\%$ $=$ $\frac{12}{100} = 0.12$
Calculate growth factor: $\newline$ $b = 1 + r$ $\newline$ $b = 1 + 0.12$ $\newline$ $b = 1.12$
Identify initial population: Identify the initial population $(a)$ . $a = 1800$
Write exponential equation: Write the exponential equation using $y = a(b)^x$ $\newline$ $y = 1800(1.12)^x$