Exponential Growth and Decay

Front

What is exponential growth?

Back

Exponential growth occurs when the increase of a quantity is proportional to its current value, leading to growth at an increasing rate over time.

Tags

CCSS.HSF-LE.A.1A

Front

What is exponential decay?

Back

Exponential decay is the decrease of a quantity at a rate proportional to its current value, resulting in a rapid decline that slows over time.

Tags

CCSS.HSF-IF.C.8B

Front

What is 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

What is 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

In the function y = 1500(1 - 0.015)^t, what does 1500 represent?

Back

The initial population of deer.

Tags

CCSS.HSF.LE.B.5

Front

In the function y = 5000(0.98)^x, what does 0.98 represent?

Back

The percentage of the account balance remaining after each year (98% of the previous amount).

Tags

CCSS.HSF.LE.B.5

Front

What does the base 'b' in an exponential function indicate?

Back

The base 'b' indicates the growth (b > 1) or decay (0 < b < 1) factor of the function.

Tags

CCSS.HSF-IF.C.8B

Front

How do you determine the initial value in an exponential function?

Back

The initial value is represented by the coefficient 'a' in the function y = a(1 ± r)^t.

Front

What is the effect of a higher growth rate on exponential growth?

Back

A higher growth rate results in a steeper increase in the quantity over time.

Tags

CCSS.HSF-IF.C.8B

Front

What is the effect of a higher decay rate on exponential decay?

Back

A higher decay rate results in a faster decrease in the quantity over time.

Tags

CCSS.HSF-IF.C.8B