Find the Domain 5000=4000(1+r(eff))^4

Problem

5000=4000*(1+(r_eff))4

Solution

1. Identify the variable for which the domain is being determined. In this equation, (r_eff) represents an effective interest rate.

2. Analyze the mathematical structure of the equation. The expression (1+(r_eff))4 is a polynomial (specifically a power function) with respect to (r_eff)

3. Determine mathematical restrictions. Polynomials are defined for all real numbers, so there are no values of (r_eff) that would result in division by zero or the square root of a negative number.

4. Consider the context of the variable. Since (r_eff) represents an interest rate, it is typically required that 1+(r_eff)>0 to ensure the base of the exponent is positive for consistent financial modeling, which implies (r_eff)>−1

5. State the domain in terms of all real numbers, as there are no algebraic undefined points in the expression (1+(r_eff))4

Final Answer

Domain:(r_eff)∈(−∞,∞)

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