Combo: Exponential Equations + Applications

Front

What is an exponential equation?

Back

An exponential equation is an equation in which a variable appears in the exponent. It can be expressed in the form y = ab^x, where a is a constant, b is the base, and x is the exponent.

Front

What does it mean for interest to be compounded quarterly?

Back

Compounded quarterly means that the interest on a loan or investment is calculated and added to the principal four times a year.

Front

How do you calculate the total amount paid on a loan with compound interest?

Back

The total amount paid can be calculated using the formula A = P(1 + r/n)^(nt), where A is the total amount, P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

Front

What is the formula for exponential growth?

Back

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

Front

What is the formula for exponential decay?

Back

The formula for exponential decay is y = a(1 - r)^t, where a is the initial amount, r is the decay rate, and t is the time.

Front

How do you find the base of an exponential function?

Back

The base of an exponential function can be found by identifying the constant factor that is raised to the power of the variable.

Front

What is the significance of the y-intercept in an exponential function?

Back

The y-intercept of an exponential function is the value of y when x = 0, which represents the initial amount before any growth or decay occurs.

Front

How do you write an exponential function given two points?

Back

To write an exponential function given two points, use the form y = ab^x and solve for a and b using the coordinates of the points.

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 time.

Front

What is the formula for calculating the population after a certain number of years with a percentage decrease?

Back

The formula is P = P0(1 - r)^t, where P0 is the initial population, r is the rate of decrease, and t is the time in years.