In Exercises 35–54, solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? S = P + Prt for r

Verified step by step guidance

1. Identify the formula given: \(S = P + Prt\). This formula is known as the simple interest formula, where \(S\) is the total amount, \(P\) is the principal, \(r\) is the interest rate, and \(t\) is the time.
2. Our goal is to solve the formula for the variable \(r\). Start by isolating terms involving \(r\) on one side. Notice that \(P\) is common in the terms \(P\) and \(Prt\).
3. Rewrite the equation by factoring out \(P\) on the right side: \(S = P(1 + rt)\).
4. Next, divide both sides of the equation by \(P\) to isolate the expression with \(r\): \(\frac{S}{P} = 1 + rt\).
5. Finally, subtract 1 from both sides and then divide by \(t\) to solve for \(r\): \(r = \frac{\frac{S}{P} - 1}{t}\).

Key Concepts

Solving Formulas for a Specific Variable

This involves isolating the desired variable on one side of the equation. Techniques include using inverse operations such as addition, subtraction, multiplication, division, and factoring to rewrite the formula explicitly in terms of that variable.

Simple Interest Formula

The formula S = P + Prt represents the simple interest calculation, where S is the total amount, P is the principal, r is the interest rate, and t is time. It calculates the total amount after interest is added linearly over time.

Algebraic Manipulation of Equations

This concept covers rearranging equations by applying algebraic rules to maintain equality. It is essential for solving for variables embedded in expressions, such as factoring out common terms or dividing both sides by a coefficient.