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Compound Interest Formula
A = P(1 + r/n)^(nt). This formula calculates the future value of an investment based on initial amount, annual interest rate, and the number of times interest is compounded per year.
Continuous Compounding Formula
A = Pe^(rt). This formula is used when interest is compounded continuously and applies the natural logarithm base 'e'.
Radioactive Decay Formula
A = Aoe^(-0.01155x). This formula models the remaining amount of radioactive material after time 'x'.
Half-Life Concept
The half-life is the time it takes for half of a substance to decay, often related to radioactive decay.
Exponential Equation Solving
To solve exponential equations, manipulate logarithms to isolate the variable, often using natural logarithm (ln) or logarithm (log).
Logarithm Change of Base Formula
logb(x) = log(x)/log(b) or ln(x)/ln(b). This formula helps evaluate logarithms with bases other than 10 or e.
Finding Intersections of Functions
Set two functions equal to each other (f(x) = g(x)) and solve for x to find their intersection points.
Natural Logarithm (ln)
Use 'ln' when dealing with the natural logarithm, especially in calculations involving the base 'e'.
Common Logarithm (log)
Use 'log' when the base of the logarithm is 10 or when base is not specified; it refers to the common logarithm.
