Exponential Functions Practice

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 it mean for a population to be increasing exponentially?

Back

It means that the population grows by a constant percentage over equal time intervals, leading to rapid growth as time progresses.

Front

What does it mean for a population to be decreasing exponentially?

Back

It means that the population decreases by a constant percentage over equal time intervals, leading to rapid decline as time progresses.

Front

What is the growth factor in an exponential function?

Back

The growth factor is the base 'b' in the function f(x) = a(b^x). If b > 1, the function represents growth; if 0 < b < 1, it represents decay.

Front

In the function f(x) = 12(1.015)^t, what does the base 1.015 represent?

Back

The base 1.015 represents a growth factor of 1.5%, indicating that the population increases by 1.5% each year.

Front

How can you identify exponential growth from a graph?

Back

Exponential growth is identified by a curve that rises steeply as x increases, showing that the values of the function increase rapidly.

Front

How can you identify exponential decay from a graph?

Back

Exponential decay is identified by a curve that falls steeply as x increases, showing that the values of the function decrease rapidly.

Front

What is the difference between exponential growth and linear growth?

Back

Exponential growth increases at a rate proportional to its current value, while linear growth increases by a constant amount.

Front

What does the expression f(x) = 2(0.85)^x represent?

Back

This expression represents exponential decay, as the base 0.85 is less than 1, indicating a decrease over time.

Front

What is the value of the growth factor in f(x) = 10(0.3)^x?

Back

The growth factor is 0.3, indicating that the function represents exponential decay.