Exponential growth and decay

Front

What is exponential growth?

Back

Exponential growth occurs when a quantity increases by a consistent percentage over a period of time, resulting in a rapid increase. The general formula is A = A₀(1 + r)^t, where A₀ is the initial amount, r is the growth rate, and t is time.

Tags

CCSS.HSF-LE.A.1A

Front

What is exponential decay?

Back

Exponential decay occurs when a quantity decreases by a consistent percentage over a period of time, leading to a rapid decrease. The general formula is A = A₀(1 - r)^t, where A₀ is the initial amount, r is the decay rate, and t is time.

Tags

CCSS.HSF-IF.C.8B

Front

How do you identify exponential growth from an equation?

Back

In an equation of the form A = A₀(1 + r)^t, if r > 0, it indicates exponential growth.

Tags

CCSS.HSF-IF.C.8B

Front

How do you identify exponential decay from an equation?

Back

In an equation of the form A = A₀(1 - r)^t, if r > 0, it indicates exponential decay.

Tags

CCSS.HSF-IF.C.8B

Front

What is the decay factor if the decay rate is 20%?

Back

The decay factor is 0.8, calculated as 1 - 0.20.

Tags

CCSS.HSF-IF.C.8B

Front

Convert 55% to a decimal.

Back

0.55, calculated by dividing 55 by 100.

Front

What does the y-intercept represent in the equation y = 4^x?

Back

The y-intercept is 1, which occurs when x = 0, giving y = 4^0 = 1.

Tags

CCSS.HSF-IF.C.7E

Front

What is the general form of an exponential function?

Back

The general form is A = A₀e^(kt), where A₀ is the initial amount, e is the base of natural logarithms, k is the growth/decay constant, and t is time.

Tags

CCSS.HSF-IF.C.8B

Front

What is the difference between growth factor and decay factor?

Back

The growth factor is (1 + r) for growth, while the decay factor is (1 - r) for decay, where r is the rate.

Tags

CCSS.HSF-IF.C.8B

Front

If a population doubles every 5 years, what is the growth rate?

Back

The growth rate can be calculated using the formula r = (2^(1/t) - 1), where t is the doubling time.