math

1. Waves from a single source: The formula used is the Wave Equation. The problem is to find the amplitude of the waves one unit away from the source. The solution is A = A0/sqrt(2). This equation states that the amplitude of the wave decreases over distance, as the inverse square of the distance between them. 2. Decaying radioactive substances: The formula used is the Half-Life Formula. The problem is to determine how long it takes for a given initial amount radioactive substance to decay to one-half its original amount. The solution is t = ln(2)/lambda, where lambda is the decay constant. This equation states that the rate of decay is exponential, with the decay rate decreasing as the original amount decreases. 3. Inflation: The formula used is the Fisher Equation. The problem is to determine how changes in interest rates and inflation affect the real rate of return for investors. The solution is R = r + (1/1+r)*inflation rate. This equation states that the real rate of return is a combination of the nominal interest rate, and the rate of inflation.