Solve the formula for $P$ given $r=-5$, $t=1.5$, and $A=21$.
$A=P(1+rt)$

• A. $P=19.5$
• B. $P=12.0$
• C. $P=22.7$
• D. $P=19.4$

Answer: (C)

Verified step by step guidance

1. Start with the given formula: \(A = P \left(1 + r t\right)\).
2. To solve for \(P\), isolate it by dividing both sides of the equation by the quantity \(\left(1 + r t\right)\), giving \(P = \frac{A}{1 + r t}\).
3. Substitute the given values into the formula: \(r = -5\), \(t = 1.5\), and \(A = 21\).
4. Calculate the expression inside the parentheses first: \(1 + r t = 1 + (-5)(1.5)\).
5. Finally, divide \(A\) by the result from step 4 to find \(P\): \(P = \frac{21}{1 + (-5)(1.5)}\).