Growth and Decay

Front

What is exponential decay?

Back

Exponential decay is a decrease in a quantity that follows an exponential function, typically represented as y = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

Front

What is the general form of an exponential decay equation?

Back

The general form is y = a(1 - r)^t or y = ae^(-kt), where 'a' is the initial value, 'r' is the decay rate, and 'k' is a positive constant.

Front

Identify the equation that represents exponential decay: y=2000(0.88) or y=0.5(1.88)

Back

y=2000(0.88) represents exponential decay.

Front

What is the starting term (a) in the function: f(x) = 300(1.16)^x?

Back

The starting term (a) is 300.

Front

Is the function f(x) = 300(1.16)^x exponential growth or decay?

Back

It is exponential growth.

Front

What is the decay rate in the equation y = 2000(0.88)?

Back

The decay rate is 0.12 (or 12%).

Front

What does the term 'exponential growth' mean?

Back

Exponential growth refers to an increase in a quantity that follows an exponential function, typically represented as y = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

Front

Identify the equation that represents exponential growth: y=2000(1.12) or y=0.5(0.88)

Back

y=2000(1.12) represents exponential growth.

Front

What is the difference between exponential growth and decay?

Back

Exponential growth increases over time, while exponential decay decreases over time.

Front

What is the value of 'r' in the equation y = 500(1 - 0.2)^t?

Back

The value of 'r' is 0.2 (or 20%).