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Suppose that $19,538 s invested at an interest rate of 6.9% per year, compounded continuously.
a) Find the exponential function that describes the amount in the account after timet, in years.
b) What is the balance after 1year? 2years? 5years? 10years?
c) What is the doubling time?
Let X be a finite dimensional linear space. Show that, for every subspace Y of X, Y perp perp = Y (that is, the annihilator of the annihilator of Y is Y)
Describe two laws of exponents and provide an example illustrating each law. Explain how to simplify the expression. How do the laws work with rational exponents?
Find the domain for each of your two rational expressions. Write the domain of each rational expression in set notation. Explain in your own words what the meaning of domain is. Also, explain why a denominator cannot be zero.
Sketch the graph of each exponential function. Sketch the graph of each logarithmic function. Evaluate log2 4x + log2 (1/x) + 2log2 (1/2).
Let a R a convex function (equivalently a concave upward function). Define
Let a subset A of the real numbers R be co-countable provided that R - A is countable. Show that the set of all countable and co-countable subsets of R is a sigma- algebra.
Isolating the natural logarithm
Comparing the 2 solution can you determine whether the fist system of equations is ill-conditioned or not?? Explain why it is ill-conditioned??
Factor the polynomial
Cramer's Rule to calculate the linear equations.
Calculation of time period
Apply the echelon method to solve the system of three equations in three unknowns.
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