If a sum of money is deposited in a savings account that is paying x percent annual interest (expressed as a decimal), then this sum of money increased by a factor of (1+x)^3 after 3 years.
A. multiply this expression
B. Evaluate the polynomial expression found in part (A) for an annual interest rate of 10% or x=0.1.
multiply the expression:
(1+x)^3
kind of pointless in this context, but
(1+x)^3 = 1 + 3x + 3x^2 + x^3
(1 + .1)^3 = 1.1^3 = 1.331
Technically, the problem is worded wrong. If the rate is x% annually, then the expression is (1 + x/100).
To multiply the expression (1+x)^3, we can use the exponentiation rule that states: (a^m)^n = a^(m*n).
In this case, we have (1+x)^3, which means (1+x) raised to the power of 3. Applying the exponentiation rule, we get:
(1+x)^3 = 1^3 * x^3
Since any number raised to the power of 1 is itself, we can simplify the expression further:
(1+x)^3 = x^3
So, the expression (1+x)^3 simplifies to x^3.
Now, let's move to the next part of the question:
Evaluate the polynomial expression found in part (A) for an annual interest rate of 10% or x=0.1.
To evaluate the polynomial expression x^3 for x=0.1, we substitute the value of x into the expression:
x^3 = (0.1)^3
To calculate this, we raise 0.1 to the power of 3:
(0.1)^3 = 0.001
Therefore, when the annual interest rate (x) is 10% or 0.1, the expression (1+x)^3 evaluates to 0.001.