Exponential Growth and Decay

Front

What is the general form of an exponential growth equation?

Back

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

Tags

CCSS.HSF-IF.C.8B

Front

What is the general form of an exponential decay equation?

Back

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

Tags

CCSS.HSF-IF.C.8B

Front

How do you calculate the growth rate from an exponential growth function?

Back

The growth rate 'r' can be found by identifying the base of the exponential function: f(x) = a(1 + r)^x.

Tags

CCSS.HSF-IF.C.8B

Front

How do you calculate the decay rate from an exponential decay function?

Back

The decay rate 'r' can be found by identifying the base of the exponential function: A = a(1 - r)^x.

Tags

CCSS.HSF-IF.C.8B

Front

What does a growth rate of 14% per week mean in an exponential growth model?

Back

It means that the quantity increases by 14% of its current value every week.

Tags

CCSS.HSF-IF.C.8B

Front

What does a decay rate of 6% per year mean in an exponential decay model?

Back

It means that the quantity decreases by 6% of its current value every year.

Tags

CCSS.HSF-IF.C.8B

Front

If a population decreases by 6% per year, how do you express this mathematically?

Back

The population can be modeled as P(t) = P0(1 - 0.06)^t, where P0 is the initial population and t is time in years.

Tags

CCSS.HSF.BF.A.2

Front

What is the significance of the base in an exponential function?

Back

The base indicates the growth or decay factor; if the base is greater than 1, it represents growth, and if it is between 0 and 1, it represents decay.

Tags

CCSS.HSF-IF.C.8B

Front

How do you find the population after a certain number of years using an exponential decay model?

Back

Substitute the number of years into the decay equation: P(t) = P0(1 - r)^t.

Front

What is the relationship between growth rate and decay rate?

Back

The growth rate is the increase in value, while the decay rate is the decrease; they are complementary in that growth rate + decay rate = 1.

Tags

CCSS.HSF-IF.C.8B