Bloom-and-Melt MabelPowerhouse · exponents and exponential functions

A crown of blooming flowers and a melting ice: growth and decay.

Exponential Growth and Decay

Growth and decay. In MathBound, the free Algebra I adventure game, Bloom-and-Melt Mabel asks these problems, and the only way past is to solve them.

Part of Exponents and Exponential Functions: chapter 7 of the standard course.

10 questions, no sign-up, nothing saved. Climbs from the basics to harder questions.

What you will practice

Growth and Decay Models. Find a value after whole periods of percent growth.

Made by the game’s own question engine. Try each one, then open its steps.

$1, 000

is

invested

at

6%

a

year

for

3

years.

How

much

more

does

it

earn

with

interest

compounded

yearly

than

with

simple

interest,

to

the

nearest

dollar?

Show the worked steps

$Compound:$ $1, 000 (1 + 0.06)^{3} \approx 1, 191;$ $simple:$ $1, 000 + 180 = 1, 180 .$
$The$ $difference$ $is$ $about$ $11$ $dollars.$

Answer: $$11$

A

culture

of

20

bacteria

doubles

every

6

hours.

How

many

bacteria

are

there

after

12

hours?

Show the worked steps

Answer: $80$

Car

A

cost

$20, 000

and

loses

15%

of

its

value

a

year.

Car

B

cost

$18, 000

and

loses

10%

a

year.

After

2

years,

which

is

worth

more,

and

by

how

much,

to

the

nearest

dollar?

Show the worked steps

$Car$ $A:$ $20, 000 (0.85)^{2} \approx 14, 450 .$ $Car$ $B : 18, 000 (0.90)^{2} \approx 14, 580 .$
$Car$ $B$ $is$ $worth$ $more,$ $by$ $about$ $130$ $dollars.$

Answer: $Car$ $B,$ $by$ $$130$

Textbook	Lessons
Standard course	7.5
Big Ideas Math Algebra 1	6.4
Big Ideas Math Algebra 1 (2022)	6.4
Carnegie Learning Algebra I	M3 2.1, M3 2.3
CPM Core Connections Algebra	5.1.3, 5.3.2, 7.1.3, 7.1.4, 11.3.5
enVision Algebra 1	6-3
enVision Algebra 1 (2024)	6-4
Eureka Math Algebra I (EngageNY)	3.4, 3.5-3.6, 3.7, 5.3, 5.8-5.9
Glencoe Algebra 1	7-6
HMH Into Algebra 1	11.1, 11.2, 11.3, 13.1
Holt McDougal Larson Algebra 1	7.4, 7.5
Illustrative Mathematics Algebra 1	5.3-5.5, 5.11-5.13, 5.14-5.15, 5.16-5.18, 5.21
Illustrative Mathematics Algebra 1 (v.360)	6.3-6.5, 6.11-6.13, 6.14-6.15, 6.16-6.18, 6.21
Math Nation Algebra 1 (Florida B.E.S.T.)	11.4, 11.6, 13.2, 13.8-13.9, 13.10
MVP Mathematics I (Integrated Math 1)	1.5, 2.6
Open Up NC Math 1 (MVP)	1.5
Pearson Algebra 1 Common Core	7-7
Reveal Algebra 1	9-3, 9-4
SpringBoard Algebra 1	23