Exponential Word Problems

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form y = a * b^x, where 'a' is a constant, 'b' is the base (a positive real number), and 'x' is the exponent.

Front

What distinguishes exponential growth from exponential decay?

Back

Exponential growth occurs when the base 'b' in the function y = a * b^x is greater than 1, while exponential decay occurs when 'b' is between 0 and 1.

Front

How can you identify if a relationship is linear, exponential, or neither from a table of values?

Back

A linear relationship has a constant rate of change, while an exponential relationship has a constant multiplicative rate of change. If neither condition is met, the relationship is neither linear nor exponential.

Front

What is the general form of an exponential growth equation?

Back

The general form of an exponential growth equation is y = a * (1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

Front

What is the formula to calculate the value of an investment after a certain number of years with exponential decay?

Back

The formula is A = P * (1 - r)^t, where 'A' is the amount after time 't', 'P' is the initial amount, 'r' is the decay rate, and 't' is time.

Front

What does the y-intercept represent in a graph of an exponential function?

Back

The y-intercept represents the initial value of the function when x = 0.

Front

How do you determine the y-intercept from an equation of an exponential function?

Back

To find the y-intercept, substitute x = 0 into the equation and solve for y.

Front

What is the significance of the base in an exponential function?

Back

The base determines the rate of growth or decay; a base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

Front

What is a common mistake when interpreting exponential functions?

Back

A common mistake is to confuse exponential growth with linear growth; exponential growth increases at an increasing rate, while linear growth increases at a constant rate.

Front

How can you graph an exponential function?

Back

To graph an exponential function, plot points for various values of x, starting from negative to positive, and connect the points to show the curve.