T2U8 Equal Differences/Equal Factors Mastery

Front

What is the definition of exponential increase?

Back

Exponential increase refers to a growth pattern where the quantity increases by a consistent percentage over a period of time, leading to rapid growth.

Front

What is the definition of linear decrease?

Back

Linear decrease refers to a decline in quantity by a constant amount over a period of time, resulting in a straight-line graph when plotted.

Front

What does it mean for a table to grow by equal factors?

Back

When a table grows by equal factors, each subsequent value is multiplied by a constant factor, indicating exponential growth.

Front

What does it mean for a table to grow by equal differences?

Back

When a table grows by equal differences, each subsequent value increases by a constant amount, indicating linear growth.

Front

How does the value of a penny that doubles every day illustrate exponential growth?

Back

The value of the penny doubles each day, demonstrating exponential growth as the increase is not linear but rather multiplicative.

Front

What is an example of exponential decrease?

Back

An example of exponential decrease is a smartphone losing one eighth of its value every year, where the decrease is proportional to its current value.

Front

What is the difference between linear and exponential growth?

Back

Linear growth increases by a constant amount, while exponential growth increases by a constant percentage, leading to much larger values over time.

Front

How can you identify if a sequence is growing by equal factors?

Back

You can identify equal factors by checking if the ratio of consecutive terms remains constant.

Front

How can you identify if a sequence is growing by equal differences?

Back

You can identify equal differences by checking if the difference between consecutive terms remains constant.

Front

What is the formula for exponential growth?

Back

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