Growth Grind Worksheet Growth Grind
Exponential Graphing Practice
NAME:
DATE:
MISSION BRIEF
Analyze each exponential function. Calculate output values for the table, identify the growth/decay type, and sketch the curve on the provided axes. Origin (0,0) is at the bottom-left corner.
1
\( y = 2(2)^x \)
Type
Growth Decay
Initial (a)
xy
2
\( y = 8(0.5)^x \)
Type
Growth Decay
Factor (b)
xy
3
\( y = 1(1.5)^x \)
Type
Growth Decay
Initial Value
xy
4
\( y = 10(0.8)^x \)
Type
Growth Decay
Factor (b)
xy
5
\( y = 0.5(3)^x \)
Type
Growth Decay
Initial Value
xy
FINANCIAL FRONTIER
6
Investment Growth
Deposit $500 at 10% interest.
Initial (a)
Rate (r)
xy
y = $200 / unit
7
Vehicle Depreciation
A $30k car loses 15% annually.
Initial (a)
Rate (r)
xy
y = $5k / unit
8
Server Farm Value
Loses 20% value every year.
Initial (a)
Rate (r)
xy
y = $1k / unit
9
Salary Compound
Start $45k with 3% annual raise.
Initial (a)
Rate (r)
xy
y = $10k / unit
10
Viral Growth
Views triple every hour. Start: 1,000.
Initial (a)
Factor (b)
xy
y = 10k views / unit
REFLECTION
How does the initial value a relate to the y-intercept on each graph?
Grind Complete
Growth Grind Answer Key Grind Master
Growth Grind Answer Key
Status
SOLVED
Abstract Equations (1-5)
1. \( y = 2(2)^x \)
GROWTH
(0, 2) | (1, 4) | (2, 8)
2. \( y = 8(0.5)^x \)
DECAY
(0, 8) | (1, 4) | (2, 2)
3. \( y = 1(1.5)^x \)
GROWTH
(0, 1) | (1, 1.5) | (2, 2.25)
4. \( y = 10(0.8)^x \)
DECAY
(0, 10) | (1, 8) | (2, 6.4)
5. \( y = 0.5(3)^x \)
GROWTH
(0, 0.5) | (1, 1.5) | (2, 4.5)
Financial Frontier (6-10)
6. Investment ($500 at 10%)
(0, $500) | (5, $805.26)
7. Car Value ($30k at -15%)
(0, $30,000) | (1, $25,500)
8. Server ($4k at -20%)
(0, $4,000) | (1, $3,200) | (2, $2,560)
9. Salary ($45k at +3%)
(0, $45,000) | (10, $60,476)
10. Viral Views (1k tripled)
(0, 1k) | (1, 3k)
Grading Standard
Math (50%)
Accurate coordinate pairs in table.
Graph (30%)
Smooth curve reflecting trend.
ID (20%)
Initial value and type identified.
Growth Grind Slides Growth
Grind
Mastering Exponential Change
The Anatomy
y = a(b)x
a
Initial Value
The starting point. On your graph, this is the y-intercept.
b
The Base
b > 1: Growth
Practice Round
Walkthrough
y = 10(2)x
a = 10 (Start)
b = 2 (Growth)
Financial Frontier
Interest
Money grows when you add the rate to 100%.
b = 1 + r
Depreciation
Value drops when you subtract the rate from 100%.
b = 1 - r
Mission: Curve Chase
Grab your worksheet. There are 10 problems waiting for you.
Ready? Go!
Function Finder Worksheet Function Finder
Exponential Construction Challenge
NAME:
DATE:
CONSTRUCTION MISSION
Analyze each scenario. Identify the initial value (a) and calculate the growth/decay factor (b). Construct the function \( y = a(b)^x \) and sketch the curve on the provided axes.
1
Initial Population: 100
Identify 'a'
Calculate 'b'
Exponential Function
y =
xy
2
Initial Value: $500
Identify 'a'
Calculate 'b'
Exponential Function
y =
xy
3
Initial Asset: $2,000
Identify 'a'
Calculate 'b'
Exponential Function
y =
xy
4
Bacteria Count: 80
Identify 'a'
Calculate 'b'
Exponential Function
y =
xy
5
Initial Price: $30,000
Identify 'a'
Calculate 'b'
Exponential Function
y =
xy
Function Finder Answer Key Function Master
Function Finder Answer Key
Status
Verified
Exponential Construction (1-10)
1. 100 growing at 5%
\( y = 100(1.05)^x \)
(0, 100) | (5, 127.63) | (10, 162.89)
2. $500 decaying at 12%
\( y = 500(0.88)^x \)
(0, 500) | (2, 387.20) | (4, 299.89)
3. $2,000 growing at 3.5%
\( y = 2,000(1.035)^x \)
(0, 2,000) | (1, 2,070) | (5, 2,375.37)
4. 80 decaying at 50%
\( y = 80(0.5)^x \)
(0, 80) | (1, 40) | (2, 20)
5. $30,000 decaying at 15%
\( y = 30,000(0.85)^x \)
(0, 30,000) | (1, 25,500) | (5, 13,311.16)
6. 10 growing at 100%
\( y = 10(2)^x \)
(0, 10) | (1, 20) | (2, 40)
7. $450 growing at 0.5%
\( y = 450(1.005)^x \)
(0, 450) | (10, 473.01) | (50, 577.50)
8. $2,500 decaying at 25%
\( y = 2,500(0.75)^x \)
(0, 2,500) | (2, 1,406.25) | (5, 593.26)
9. $1,200 decaying at 90%
\( y = 1,200(0.1)^x \)
(0, 1,200) | (1, 120) | (2, 12)
10. 5 growing at 25%
\( y = 5(1.25)^x \)
(0, 5) | (1, 6.25) | (5, 15.26)
Assessment Criteria
Factor Calculation
Convert % to decimal and add/subtract from 1. Watch for 0.5% (0.005) and 100% (doubling logic, factor = 2).
Function Form
Ensure correct form: \( y = a(b)^x \). Large numbers and decimals must be accurately placed.
