Q2: Pre-AP Algebra 2 Retake on Flashcard#1 for Unit 1: L1.4-L1.5

Front

What is exponential decay?

Back

Exponential decay is a decrease in a quantity by a consistent percentage over a period of time, often modeled by the equation A = A0 * e^(-kt), where A0 is the initial amount, k is the decay constant, and t is time.

Front

How do you calculate the population after a certain number of years with exponential decay?

Back

To calculate the population after a certain number of years with exponential decay, use the formula P = P0 * (1 - r)^t, where P0 is the initial population, r is the decay rate (as a decimal), and t is the number of years.

Front

What is the formula for exponential growth?

Back

The formula for exponential growth is A = A0 * e^(kt), where A0 is the initial amount, k is the growth constant, and t is time.

Front

How do you determine if a model represents exponential growth or decay?

Back

A model represents exponential growth if the base of the exponent is greater than 1 (e.g., A = A0 * (1 + r)^t) and decay if the base is between 0 and 1 (e.g., A = A0 * (1 - r)^t).

Front

What is the significance of the decay rate in exponential decay problems?

Back

The decay rate indicates the percentage decrease of the quantity per time period. A higher decay rate results in a faster decrease in the quantity.

Front

What does the term 'exponential regression' refer to?

Back

Exponential regression is a statistical method used to model data that follows an exponential trend, allowing for the prediction of future values based on past data.

Front

How can you interpret the parameters in the equation y = a(b)^x?

Back

In the equation y = a(b)^x, 'a' represents the initial value, 'b' is the growth (b > 1) or decay (0 < b < 1) factor, and 'x' is the independent variable, often representing time.

Front

What is the initial value in an exponential model?

Back

The initial value in an exponential model is the value of the quantity at time t = 0, often denoted as A0.

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

How do you find the equation of an exponential function from data points?

Back

To find the equation of an exponential function from data points, you can use methods such as logarithmic transformation or statistical software to perform exponential regression.