Exponential Growth or Decay Flashcard

Front

Classify the model as Exponential GROWTH or DECAY: A=1200(0.85)^6

Back

Decay

Front

Daniel’s Print Shop purchased a new printer for $35,000. Each year it depreciates at a rate of 5%. How much will the printer be worth in 8 years?

Back

$23,219.72

Front

Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.

Back

y=5000(0.7)^x

Front

What is the Growth/Decay PERCENT of the following exponential function: f(x)=125(0.85)^x?

Back

15%

Front

What does the 'a' in y=a(1+r)^x represent?

Back

Initial Amount

Front

Define Exponential Growth.

Back

Exponential growth occurs when the growth rate of a value is proportional to its current value, leading to growth that accelerates over time.

Front

Define Exponential Decay.

Back

Exponential decay occurs when a quantity decreases at a rate proportional to its current value, leading to a rapid decrease over time.

Front

What is the formula for Exponential Growth?

Back

y = a(1 + r)^x, where 'a' is the initial amount, 'r' is the growth rate, and 'x' is time.

Front

What is the formula for Exponential Decay?

Back

y = a(1 - r)^x, where 'a' is the initial amount, 'r' is the decay rate, and 'x' is time.

Front

If a population of 1000 increases by 20% each year, what will be the population after 3 years?

Back

y = 1000(1.2)^3 = 1728.