Exponential Functions

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 the base (a positive real number), and 'x' is the exponent.

Front

What does the 'a' represent in the function f(x) = a(b^x)?

Back

The 'a' represents the initial value or the y-intercept of the exponential function.

Front

What is the base in an exponential function?

Back

The base 'b' in an exponential function determines the rate of growth or decay. If b > 1, the function represents exponential growth; if 0 < b < 1, it represents exponential decay.

Front

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

Back

An exponential function will show a constant multiplicative rate of change between consecutive values, rather than a constant additive rate.

Front

What is the general form of an exponential growth function?

Back

The general form of an exponential growth function is f(x) = a(1 + r)^x, where 'r' is the growth rate.

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 of the current value.

Front

What does it mean if an exponential function has a base less than 1?

Back

If the base is less than 1, the function represents exponential decay, meaning the value decreases over time.

Front

How can you graph an exponential function?

Back

To graph an exponential function, plot points for various values of x, then connect them to show the curve that rises or falls steeply.

Front

What is the y-intercept of the function f(x) = 300(1.16)^x?

Back

The y-intercept is 300, which is the value of f(0) when x = 0.

Front

What is the domain of an exponential function?

Back

The domain of an exponential function is all real numbers (-∞, ∞).