P dollars is invested at annual interest rate r for 1 year. If the interest is compounded semiannually, then the polynomial P(q + r/2)^2 represents the value of the investment after 1 year. Rewrite w/o parenthesis and eval if P= $200 and r = 10%
P(1 + r/2)^2
200(1 + r/0.10/2)^2
(200 + r/20)^2
?????
To rewrite the expression without parentheses, follow the order of operations (PEMDAS):
Step 1: Simplify the expression inside the parentheses.
r/0.10/2 can be simplified to r/0.05, which equals 20r.
Step 2: Substitute the simplified expression into the original expression.
(200 + r/20)^2 becomes (200 + 20r)^2.
Step 3: Evaluate the expression using the given values.
If P = $200 and r = 10% (or 0.10 as a decimal), substitute these values into the expression:
(200 + 20(0.10))^2 = (200 + 2)^2 = 202^2 = 40,804.
Therefore, the simplified expression evaluated with P = $200 and r = 10% is 40,804.