Growth or 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.

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.

Tags

CCSS.HSF-IF.C.8B

Front

How can you identify if a function represents growth or decay?

Back

If the base of the exponential function is greater than 1, it represents growth. If the base is between 0 and 1, it represents decay.

Tags

CCSS.HSF-IF.C.8B

Front

What does the y-intercept represent in an exponential function?

Back

The y-intercept represents the initial value of the function when x=0.

Tags

CCSS.HSF-IF.C.7E

Front

In the equation y = a(b^x), what does 'a' represent?

Back

'a' represents the initial amount or the y-intercept of the function.

Tags

CCSS.HSF.LE.B.5

Front

In the equation A = P(1 + r)^t, what does 'r' represent?

Back

'r' represents the rate of growth in decimal form.

Front

In the equation A = P(1 - r)^t, what does 'r' represent?

Back

'r' represents the rate of decay in decimal form.

Front

What is the decay rate in the model A = 1200(0.85)^6?

Back

The decay rate is 0.15, which is calculated as 1 - 0.85.

Tags

CCSS.HSF-IF.C.8B

Front

What is the growth factor in the equation y = 5(1.04)^x?

Back

The growth factor is 1.04.

Tags

CCSS.HSF-IF.C.8B

Front

What is the formula for calculating the amount after n periods of growth?

Back

A = P(1 + r)^n, where A is the amount, P is the principal, r is the growth rate, and n is the number of periods.

Tags

CCSS.HSF.BF.A.2