11/21 Flashcard on Exponential Functions (Quizizz)

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a * b^x, where a is a constant, b is a positive real number, and x is the exponent. It shows rapid growth or decay.

Front

How can you identify an exponential function from a table of values?

Back

In a table of values, an exponential function will show a constant ratio between consecutive outputs (y-values) when the inputs (x-values) are equally spaced.

Front

What is the general form of an exponential decay function?

Back

The general form of an exponential decay function is f(t) = a * (1 - r)^t, where a is the initial amount, r is the decay rate, and t is time.

Front

What does the base of an exponential function represent?

Back

The base of an exponential function indicates the growth (if greater than 1) or decay (if between 0 and 1) rate of the function.

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 faster growth over time.

Front

What is the formula for exponential growth?

Back

The formula for exponential growth is f(t) = a * (1 + r)^t, where a is the initial amount, r is the growth rate, and t is time.

Front

How do you write an exponential function for depreciation?

Back

An exponential function for depreciation can be written as f(t) = P * (1 - r)^t, where P is the initial value, r is the depreciation rate, and t is time.

Front

What is the value of a car worth $15,000 after 1 year if it depreciates at 8%?

Back

The value after 1 year is f(1) = 15,000 * (0.92)^1 = $13,800.

Front

What does it mean if a population is decreasing at a rate of 3.5% per year?

Back

It means that each year, the population is 96.5% of the previous year's population, modeled by L(t) = L0 * (1 - 0.035)^t.

Front

How can you determine if a graph represents an exponential function?

Back

A graph represents an exponential function if it shows a curve that rises or falls sharply, rather than a straight line.