Problem 49 - Algebra and Trigonometry

Question

Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? \(S=P+P r t\) for \(r\)

Step-by-Step Solution

Answer

The value of 'r' from the formula \(S=P+P r t\) is \(r = \frac{S - P}{P t}\). It shows that the formula describes the calculation of interest rate in a compound interest scenario.

Step 1: Understand the Problem

The goal is to rearrange the formula \(S=P+P r t\) to isolate 'r'. This would involve first subtracting 'P' from both sides, and then dividing both sides by 'P t'.

Step 2: Subtract 'P' from Both Sides of the Formula

When 'P' is subtracted from both sides of the formula, it gives \(S - P = P r t\). This step helps to eliminate 'P' from the left side of the equation.

Step 3: Divide Through by 'P t'

Next, divide both sides of the equation by 'P t' to isolate 'r'. This gives \(r = \frac{S - P}{P t}\). This is the simplified form of the formula needed.