Growth/Decay Review

Front

What is Exponential Growth?

Back

Exponential Growth occurs when a quantity increases by a fixed percentage over a period of time, resulting in a rapid increase as the quantity grows.

Front

What is Exponential Decay?

Back

Exponential Decay occurs when a quantity decreases by a fixed percentage over a period of time, leading to a rapid decrease as the quantity diminishes.

Front

What is the formula for Exponential Growth?

Back

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

Front

What is the formula for Exponential Decay?

Back

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

Front

What does the variable 'a' represent in exponential functions?

Back

The variable 'a' represents the initial amount or starting value in an exponential function.

Front

How do you identify the growth factor in an exponential function?

Back

The growth factor is found in the expression (1 + r) in the formula y = a(1 + r)^t.

Front

What is the growth factor in the function y = 0.3(1.08)^x?

Back

The growth factor is 1.08.

Front

How do you write an exponential function for a situation with a known initial amount and growth rate?

Back

Use the formula y = a(1 + r)^t, substituting 'a' for the initial amount and 'r' for the growth rate.

Front

What is the initial amount in the function f(x) = 300(1.16)^x?

Back

The initial amount is 300.

Front

If Samantha's hair grows at a rate of 14% a week, how would you model this with an exponential function?

Back

The model would be y = 6(1.14)^x, where 6 is the initial length in inches.