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.

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.

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.

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.

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.

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.

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.

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.

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.