Exponential Equations

Front

What is an exponential equation?

Back

An exponential equation is an equation in which a variable appears in the exponent. For example, y = a(b^x) where a and b are constants.

Front

What is the general form of an exponential function?

Back

The general form of an exponential function is f(x) = a(b^x), where a is a constant, b is the base (b > 0), and x is the exponent.

Front

What does the base of an exponential function represent?

Back

The base of an exponential function represents the growth factor. If the base is greater than 1, the function models exponential growth; if it is between 0 and 1, it models exponential decay.

Front

How do you solve an exponential equation with the same base?

Back

To solve an exponential equation with the same base, set the exponents equal to each other and solve for the variable.

Front

What is the growth factor in an exponential function?

Back

The growth factor is the constant multiplier in the function, represented by the base of the exponent. For example, in f(x) = a(b^x), b is the growth factor.

Front

What is the formula for compound interest?

Back

The formula for compound interest is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, P is the principal amount, 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

How do you express exponential growth in a word problem?

Back

Exponential growth can be expressed as f(t) = a(1 + r)^t, where a is the initial amount, r is the growth rate, and t is time.

Front

What is the value of x in the equation 5^(2x) = 5^(-x)?

Back

x = 0.

Front

If a population doubles every year, how can this be represented mathematically?

Back

This can be represented as P(t) = P_0(2^t), where P_0 is the initial population and t is the number of years.

Front

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

Back

The exponent indicates the number of times the base is multiplied by itself, which affects the rate of growth or decay.