# Write Exponential Functions For Word Problems Worksheet

## 6 problems

To write exponential functions for word problems, identify the initial value and growth or decay factor. Use the form $$f(x) = a \cdot b^x$$, where $$a$$ is the initial value and $$b$$ is the growth or decay rate. This approach helps model real-life scenarios involving exponential change. A write exponential functions for word problems worksheet offers practice, while a write exponential functions for word problems pdf provides a downloadable guide.

Algebra 2
Exponential Functions

## 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.

## How to Write Exponential Functions for Word Problems?

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

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