Exponentials: Which Model?

Presentation

•

Mathematics

•

9th - 12th Grade

•

Practice Problem

•

Medium

•

CCSS

HSF.LE.A.2

Standards-aligned

Nicole Frye

Used 6+ times

FREE Resource

2 Slides • 9 Questions

Which model is it?

Determining when to use each exponential model

Multiple Choice

For the situation below, identify the type of equation you would apply.

Your new computer costs $174 (It’s a Chromebook ☹️) but it loses value by about 11% each year.

$y=a\left(b\right)^x$

b = 1 + r

(appreciate)

$y=a\left(b\right)^x$

b = 1 - r

(depreciate)

$y=a\left(b\right)^x$

$b=\frac{\ 1}{2}$

x = (x/ half-life)

(half-life)

$y=a\left(e\right)^{rt}$

b = e

the natural base

(continuous)

Multiple Choice

For the situation below, identify the type of equation you would apply.

Phosphorus-32 is used to study a plant’s use of fertilizer.

It has a half-life of 14.3 days and we have a 75 g sample.

$y=a\left(b\right)^x$

b = 1 + r

(appreciate)

$y=a\left(b\right)^x$

b = 1 - r

(depreciate)

$y=a\left(b\right)^x$

$b=\frac{\ 1}{2}$

x = (x/ half-life)

(half-life)

$y=a\left(e\right)^{rt}$

b = e

the natural base

(continuous)

Multiple Choice

For the situation below, identify the type of equation you would apply.

The population of St. Louis in 1950 was 856,796. Since then, it has been decreasing; in 2010, the population fell to 319,365. Determine the rate of decline in the population.

$y=a\left(b\right)^x$

b = 1 + r

(appreciate)

$y=a\left(b\right)^x$

b = 1 - r

(depreciate)

$y=a\left(b\right)^x$

$b=\frac{\ 1}{2}$

x = (x/ half-life)

(half-life)

$y=a\left(e\right)^{rt}$

b = e

the natural base

(continuous)

Multiple Choice

For the situation below, identify the type of equation you would apply.

Mrs. Lindsey bought a Scandinavian bookshelf and its value is declines at a rate of 10% per year. After 8 years it was worth $13,000.

$y=a\left(b\right)^x$

b = 1 + r

(appreciate)

$y=a\left(b\right)^x$

b = 1 - r

(depreciate)

$y=a\left(b\right)^x$

$b=\frac{\ 1}{2}$

x = (x/ half-life)

(half-life)

$y=a\left(e\right)^{rt}$

b = e

the natural base

(continuous)

Multiple Choice

For the situation below, identify the type of equation you would apply.

Suppose Mr. Covey purchased land in 2005 for $25,000.

His land is in San Fran and it gains value annually at 4.2%.

$y=a\left(b\right)^x$

b = 1 + r

(appreciate)

$y=a\left(b\right)^x$

b = 1 - r

(depreciate)

$y=a\left(b\right)^x$

$b=\frac{\ 1}{2}$

x = (x/ half-life)

(half-life)

$y=a\left(e\right)^{rt}$

b = e

the natural base

(continuous)

Multiple Choice

For the situation below, identify the type of equation you would apply.

Anthony invested in an account paying 5% interest compounded continuously. If he’d like the account to have $32,000 so he can buy a new Daytona Charger in 5 years, how much should he invest?

$y=a\left(b\right)^x$

b = 1 + r

(appreciate)

$y=a\left(b\right)^x$

b = 1 - r

(depreciate)

$y=a\left(b\right)^x$

$b=\frac{\ 1}{2}$

x = (x/ half-life)

(half-life)

$y=a\left(e\right)^{rt}$

b = e

the natural base

(continuous)

Multiple Choice

For the situation below, identify the type of equation you would apply.

The world population in 2000 was approximately 6.08 billion.

The annual rate of increase was about 1.26%.

$y=a\left(b\right)^x$

b = 1 + r

(appreciate)

$y=a\left(b\right)^x$

b = 1 - r

(depreciate)

$y=a\left(b\right)^x$

$b=\frac{\ 1}{2}$

x = (x/ half-life)

(half-life)

$y=a\left(e\right)^{rt}$

b = e

the natural base

(continuous)

Multiple Choice

For the situation below, identify the type of equation you would apply.

A painting was purchased at an art exhibition.

Afterwards, it's value increases by 15% each year.

$y=a\left(b\right)^x$

b = 1 + r

(appreciate)

$y=a\left(b\right)^x$

b = 1 - r

(depreciate)

$y=a\left(b\right)^x$

$b=\frac{\ 1}{2}$

x = (x/ half-life)

(half-life)

$y=a\left(e\right)^{rt}$

b = e

the natural base

(continuous)

Poll

At present, which model do you feel is the most challenging to work with?

$y=a\left(b\right)^x$

b = 1 +/- r

(appreciate/depreciate)

$y=a\left(b\right)^x$

$b=\frac{\ 1}{2}$

x = (x/ half-life)

(half-life)

$y=a\left(e\right)^{rt}$

b = e

the natural base

(continuous)

None! They all make sense!

None!

They all make sense!

Closing Thoughts:

What information helps you determine which variation to use for exponential modeling problems?

Reminder, the models are:

Appreciate/Depreciate: y = a(b)^x where b = 1 +/- r

Natural/Continuous: y = a(e)^rt where the rate is part of the exp.

Half-Life Decay: y=a(b)^x/half-life where b=1/2

Which model is it?

Determining when to use each exponential model

Show answer

Auto Play

Slide 1 / 11

SLIDE

Similar Resources on Wayground

9 questions

estimating large numbers

Presentation

•

9th - 12th Grade

9 questions

U7L4 Tangent Lines

Presentation

•

9th - 12th Grade

10 questions

6.4 Rational Exponents (Part 1)

Presentation

•

9th - 12th Grade

9 questions

Geo Review 8-2-8-4

Presentation

•

9th - 12th Grade

9 questions

Solving Quadratic Equations

Presentation

•

9th - 12th Grade

10 questions

Graphing Parallel and Perpendicular Lines

Presentation

•

9th - 12th Grade

8 questions

Pythagorean Theorem

Presentation

•

9th - 12th Grade

10 questions

3x3 Word Problems

Presentation

•

9th - 12th Grade

Popular Resources on Wayground

10 questions

Safety Day 2026 – Student Review

Quiz

•

9th Grade

21 questions

Continents and Oceans

Quiz

•

6th Grade

20 questions

Parts of Speech

Quiz

•

5th Grade

16 questions

Subject & Predicate

Quiz

•

5th Grade

25 questions

Multiplication Facts

Quiz

•

5th Grade

12 questions

Map Skills

Quiz

•

3rd Grade

22 questions

Continents and Oceans

Quiz

•

5th Grade

15 questions

Rounding Decimals

Quiz

•

5th Grade

Discover more resources for Mathematics

12 questions

Absolute Value Equations

Quiz

•

9th Grade

20 questions

Function or Not a Function

Quiz

•

8th - 9th Grade

11 questions

Slope from 2 points

Quiz

•

8th - 9th Grade

10 questions

Exploring the Basics of Exponents

Interactive video

•

6th - 10th Grade

10 questions

Solving Absolute Value Equations

Quiz

•

9th Grade

20 questions

Unit 5 Test RSC (25-26)

Quiz

•

10th Grade

18 questions

SB 12.2 Write in point slope form

Quiz

•

9th Grade

12 questions

Identify Rigid Transformations

Quiz

•

8th - 12th Grade