Solve 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, in the equation 2^x = 8, x is the variable in the exponent.

Front

What is the general form of an exponential decay equation?

Back

The general form of an exponential decay equation is A(t) = A_0 * e^(-kt), where A_0 is the initial amount, k is the decay constant, and t is time.

Front

How do you solve the equation 7^(-x) = 49?

Back

To solve 7^(-x) = 49, rewrite 49 as 7^2. Thus, -x = 2, leading to x = -2.

Front

What is the value of 2^x when x = 3?

Back

When x = 3, 2^x = 2^3 = 8.

Front

How do you rewrite the number 8 as a power of 2?

Back

8 can be rewritten as 2^3.

Front

What is the property of exponents that states a^m * a^n = a^(m+n)?

Back

This property is known as the Product of Powers Property.

Front

How do you solve the equation 2^x = 4^(x+1)?

Back

Rewrite 4 as 2^2, so the equation becomes 2^x = (2^2)^(x+1) = 2^(2x + 2). Set the exponents equal: x = 2x + 2, leading to x = -2.

Front

What is the base of the exponential function in the equation 9^(8-x) = 27^(x-3)?

Back

The bases are 9 and 27, which can be rewritten as 3^2 and 3^3 respectively.

Front

How do you solve the equation 9^(8-x) = 27^(x-3)?

Back

Rewrite 9 as 3^2 and 27 as 3^3. The equation becomes (3^2)^(8-x) = (3^3)^(x-3). Set the exponents equal: 2(8-x) = 3(x-3). Solve for x to find x = 5.

Front

What is the Exponential Growth Formula?

Back

The Exponential Growth Formula is A(t) = A_0 * e^(kt), where A_0 is the initial amount, k is the growth rate, and t is time.