Writing Exponential Equations Practice

Front

What is an exponential equation?

Back

An exponential equation is a mathematical expression in which a variable appears in the exponent. It typically has the form y = a(b)^x, where a is a constant, b is the base, and x is the exponent.

Front

How do you write an exponential decay equation?

Back

An exponential decay equation can be written as y = a(1 - r)^x, where a is the initial amount, r is the decay rate, and x is the time period.

Front

What is the y-intercept in an exponential function?

Back

The y-intercept is the initial value of the function when x = 0. In the function f(x) = a(b)^x, the y-intercept is equal to a.

Front

What does it mean for a quantity to double?

Back

Doubling means that the quantity increases by 100%. In an exponential growth equation, this is represented by a base greater than 1.

Front

What is the formula for exponential growth?

Back

The formula for exponential growth is y = a(1 + r)^x, where a is the initial amount, r is the growth rate, and x is the time period.

Front

How do you identify exponential decay from a graph?

Back

Exponential decay is identified by a graph that decreases rapidly at first and then levels off, approaching zero but never touching the x-axis.

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 over equal intervals.

Front

How do you write an exponential growth equation for a population?

Back

An exponential growth equation for a population can be written as P(t) = P0(1 + r)^t, where P0 is the initial population, r is the growth rate, and t is time.

Front

What is the decay factor in an exponential decay equation?

Back

The decay factor is represented as (1 - r), where r is the decay rate. It indicates the fraction of the quantity that remains after each time period.

Front

How do you determine the initial value from an exponential function?

Back

The initial value can be determined by evaluating the function at x = 0. For example, in f(x) = a(b)^x, the initial value is a.