Question

exponential growth vs. exponential decay
drag and drop each card to attach it to either the exponential growth or exponential decay card.
you should only be creating 2 piles of cards.
you do not have all of the cards sorted correctly yet. keep sorting!
exponential decay
a pesticide kills an ant population
at a rate of 15% per day from the
time of its application
5% depreciation per
year
$f(x)=a(1 - r)^x$,
where $r > 0$.
$y = 5(1 - 8\\%)$
one u.s. dollar has
about 2 - 3% less
purchasing power
each year.
$y = 5(1 + 8\\%)^x$
a population of bunny
rabbits grows by 60%
every year
$v = 60000(0.85)^x$
$s = 5000(1.04)^x$
$f(x)=a(1 + r)^x$,
where $r > 0$.
exponential growth
growth of 5% per year
inflation increases the costs of
goods about 2 - 3% per year.

Explanation:

Step1: Recall Exponential Formulas

Exponential decay: \( f(x)=a(1 - r)^x \) (\( r>0 \)), represents decrease.
Exponential growth: \( f(x)=a(1 + r)^x \) (\( r>0 \)), represents increase.

Step2: Sort Each Card

• Exponential Decay:
• "5% depreciation per year" (depreciation = decay).
• "A pesticide kills an ant population at 15% per day" (population decreases).
• \( f(x)=a(1 - r)^x, r>0 \) (decay formula).
• \( y = 5(1 - 8\%)^x \) (uses \( 1 - r \), decay).
• "One U.S. dollar has 2 - 3% less purchasing power" (value decreases).
• \( V = 60000(0.85)^x \) (0.85 = \( 1 - 0.15 \), decay).

• Exponential Growth:
• \( y = 5(1 + 8\%)^x \) (uses \( 1 + r \), growth).
• "A population of bunnies grows by 60% yearly" (population increases).
• "Growth of 5% per year" (growth).
• \( S = 5000(1.04)^x \) (1.04 = \( 1 + 0.04 \), growth).
• \( f(x)=a(1 + r)^x, r>0 \) (growth formula).
• "Inflation increases costs by 2 - 3% yearly" (costs increase).

Answer:

Exponential Decay Cards:

• 5% depreciation per year
• A pesticide kills an ant population at a rate of 15% per day from the time of its application
• \( f(x) = a(1 - r)^x \), where \( r > 0 \)
• \( y = 5(1 - 8\%)^x \)
• One U.S. dollar has about 2 - 3% less purchasing power each year
• \( V = 60000(0.85)^x \)

Exponential Growth Cards:

• \( y = 5(1 + 8\%)^x \)
• A population of bunny rabbits grows by 60% every year
• Growth of 5% per year
• \( S = 5000(1.04)^x \)
• \( f(x) = a(1 + r)^x \), where \( r > 0 \)
• Inflation increases the costs of goods about 2 - 3% per year