Exponential 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. For example, if a population doubles every year, it is experiencing exponential growth.

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. For example, radioactive substances decay at a rate proportional to their current amount.

Tags

CCSS.HSF-IF.C.8B

Front

Write the general formula for exponential growth.

Back

y = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

Tags

CCSS.HSF-IF.C.8B

Front

Write the general formula for exponential decay.

Back

y = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

Tags

CCSS.HSF-IF.C.8B

Front

What does the base of an exponential function represent?

Back

The base of an exponential function indicates the growth or decay factor. A base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

Tags

CCSS.HSF-IF.C.8B

Front

How do you determine the y-intercept of an exponential function?

Back

The y-intercept of an exponential function can be found by evaluating the function at t=0. For example, in y = a(1 + r)^t, the y-intercept is 'a'.

Tags

CCSS.HSF-IF.C.7E

Front

What is the y-intercept of the function y = 7(5/4)^x?

Back

The y-intercept is 7, as it is the value of the function when x = 0.

Tags

CCSS.HSF-IF.C.7E

Front

If a quantity doubles every week, what expression represents its size after 'n' weeks?

Back

The expression is y = a(2)^n, where 'a' is the initial size.

Tags

CCSS.HSF.BF.A.2

Front

What is the difference between linear and exponential functions?

Back

Linear functions increase or decrease by a constant amount, while exponential functions increase or decrease by a constant percentage.

Front

What is the growth rate in the equation y = 6(1.14)^x?

Back

The growth rate is 14%, as indicated by the factor (1 + 0.14) in the equation.

Tags

CCSS.HSF-IF.C.8B