Exponential Growth and Decay
Presentation
•
Mathematics
•
9th Grade
•
Medium
Standards-aligned
Daylan Hatcherson
Used 4+ times
FREE Resource
5 Slides • 9 Questions
1
2
y = a(b)x
The 'b' is (1 - r)
DECAY: y = a(1 - r)x
Decay
y = a(b)x
The 'b' is (1 + r)
GROWTH: y = a(1 + r)x
Growth
3
1: Decide if the problem is describing exponential growth or decay. ("increase" = growth, "decrease" = decay)
2: Convert the growth or decay percentage to a decimal. This decimal is your r value. Ex: 23% = .23 and 5% = .05
3: Write your exponential equation. a is your starting value.
GROWTH: y = a(1 + r)^x
DECAY: y = a(1 - r)^x
4
Multiple Choice
Mr. Hatcherson currently brings in an annual salary of $55,000 and anticipates a raise of 5% every year.
Is this problem describing exponential growth or decay?
Growth
Decay
5
Fill in the Blanks
Mr. Hatcherson currently brings in an annual salary of $55,000 and anticipates a raise of 5% every year.
Convert the growth percentage to a decimal.
Type answer...
6
Fill in the Blanks
Mr. Hatcherson currently brings in an annual salary of $55,000 and anticipates a raise of 5% every year.
We now know that our r value is 0.05. What is our a value? (a is the starting value)
Type answer...
7
Draw
Mr. Hatcherson currently brings in an annual salary of $55,000 and anticipates a raise of 5% every year.
Okay, now we know this is growth, r = 0.05, and a = 55,000. Let's put it all together in an exponential equation.
8
9
Multiple Choice
Mr. Hatcherson got a promotion because of all of his students passed the STAAR Test and is now a real-deal teacher. He purchased a Hellcat for $90,000 and anticipates that it will depreciate 15% every year.
Is this problem describing exponential growth or decay?
Growth
Decay
10
Fill in the Blanks
Mr. Hatcherson got a promotion because of all of his students passed the STAAR Test and is now a real-deal teacher. He purchased a Hellcat for $90,000 and anticipates that it will depreciate 15% every year.
Convert the decay percentage to a decimal.
Type answer...
11
Fill in the Blanks
Mr. Hatcherson got a promotion because of all of his students passed the STAAR Test and is now a real-deal teacher. He purchased a Hellcat for $90,000 and anticipates that it will depreciate 15% every year.
We now know that our r value is 0.15. What is our a value? (a is the starting value)
Type answer...
12
Draw
Mr. Hatcherson got a promotion because of all of his students passed the STAAR Test and is now a real-deal teacher. He purchased a Hellcat for $90,000 and anticipates that it will depreciate 15% every year.
Okay, now we know this is decay, r = 0.15, and a = 90,000. Let's put it all together in an exponential equation.
13
14
Fill in the Blanks
Mr. Hatcherson got a promotion because of all of his students passed the STAAR Test and is now a real-deal teacher. He purchased a Hellcat for $90,000 and anticipates that it will depreciate 15% every year.
Even though Mr. Hatcherson now has the coolest car on campus, what will the car be worth after 5 years?
(Hint): Round your answer to the nearest whole number
Type answer...
Show answer
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