Exponential Equations w/ Percents

Front

What is an exponential equation?

Back

An exponential equation is a mathematical expression in which a variable appears in the exponent. It can be represented in the form y = a * b^x, where 'a' is a constant, 'b' is the base, and 'x' is the exponent.

Front

How do you represent a decay rate in an exponential equation?

Back

A decay rate can be represented in an exponential equation by using a base less than 1. For example, if a quantity decreases by 20%, the base would be 0.8 (1 - 0.2). The equation would be y = a * (0.8)^x.

Front

What does the variable 'b' represent in the equation y = a * b^x?

Back

In the equation y = a * b^x, 'b' represents the growth (if b > 1) or decay (if 0 < b < 1) factor of the exponential function.

Front

If a population of butterflies is declining at a rate of 68%, what is the base for the exponential equation?

Back

The base for the exponential equation would be 0.32, since 1 - 0.68 = 0.32.

Front

Write an exponential equation for a population of 150 million butterflies declining at 68%.

Back

The equation is y = 150 * (0.32)^x.

Front

What is the formula for calculating the value of an investment after a percentage decrease?

Back

The formula is y = P * (1 - r)^t, where P is the initial amount, r is the rate of decrease, and t is the time.

Front

If an investment of $1200 loses 12% of its value each month, what is the exponential equation?

Back

The equation is y = 1200 * (0.88)^x.

Front

How do you determine if a function is linear or exponential?

Back

A function is exponential if it can be expressed in the form y = a * b^x, where 'b' is a constant base. If it can be expressed as y = mx + b, it is linear.

Front

What is the value of 'b' in the equation for a land price increasing by 1.5% each year?

Back

The value of 'b' is 1.015, representing a 1.5% increase.

Front

Write an exponential equation for a function that decays by 33% starting at 650.

Back

The equation is y = 650 * (0.67)^x.