Algebra 1: Linear vs. Exponential Functions

Front

What is the general form of an exponential growth function?

Back

The general form of an exponential growth function is y = a(1 + r)^x, where 'a' is the initial amount, 'r' is the growth rate, and 'x' is the time in years.

Front

What is the general form of an exponential decay function?

Back

The general form of an exponential decay function is y = a(1 - r)^x, where 'a' is the initial amount, 'r' is the decay rate, and 'x' is the time in years.

Front

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

Back

If the base of the exponential function is greater than 1, it represents exponential growth. If the base is between 0 and 1, it represents exponential decay.

Front

What is the percent increase in an exponential growth function with a growth factor of 1.80?

Back

The percent increase is 80%, calculated as (1.80 - 1) * 100%.

Front

What is the percent decrease in an exponential decay function with a decay factor of 0.75?

Back

The percent decrease is 25%, calculated as (1 - 0.75) * 100%.

Front

How can you model the value of an investment that grows at a constant percentage rate annually?

Back

You can model it using the equation y = P(1 + r)^t, where P is the principal amount, r is the annual interest rate, and t is the number of years.

Front

What does the variable 'x' typically represent in exponential functions?

Back

In exponential functions, 'x' typically represents time, often measured in years.

Front

What is the significance of the initial value 'a' in an exponential function?

Back

The initial value 'a' represents the starting amount or value before any growth or decay occurs.

Front

How do you find the remaining amount after a certain number of periods in a decay scenario?

Back

You can find the remaining amount using the formula y = a(1 - r)^x, where 'a' is the initial amount, 'r' is the decay rate, and 'x' is the number of periods.

Front

What is the relationship between linear and exponential functions in terms of growth?

Back

Linear functions grow by a constant amount over equal intervals, while exponential functions grow by a constant percentage, leading to faster growth over time.