Modeling Exponential Growth and Decay

Front

What is the general 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

What is the general 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

How do you convert a percentage to a decimal?

Back

Divide the percentage by 100. For example, 11.2% becomes 0.112.

Front

If a quantity decreases by 30% each year, what is the decay factor?

Back

The decay factor is 0.70 (1 - 0.30).

Front

What does it mean for a quantity to double?

Back

It means the quantity increases by 100% over a given time period.

Front

How do you calculate the value of an asset after depreciation?

Back

Use the formula: Value = Initial Value * (1 - r)^t, where 'r' is the depreciation rate and 't' is time.

Front

What is the value of a $35,000 printer after 8 years with a 5% annual depreciation?

Back

$23,219.72.

Front

What is the growth factor for a quantity that doubles every week?

Back

The growth factor is 2.

Front

If a culture of bacteria starts with 5000 cells and dies by 30% each year, what is the equation representing this situation?

Back

y = 5000(1 - 0.30)^x.

Front

What is the expression for the size of a peach that doubles in size every week after 5 weeks if it starts at 70 inches?

Back

70(2)^5.