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Classify each of the following statements as either true or false. To solve an exponential equation, we can take the common logarithm of both sides of the equation.

Student Loan Repayment. A college loan of 29,000 dollars is made at \(3 \%\) interest, compounded annually. After \(t\) years, the amount due, \(A,\) is given by the function $$ A(t)=29,000(1.03)^{t} $$ a) After what amount of time will the amount due reach \(\$ 35,000 ?\) b) Find the doubling time.

The number of people who have heard a rumor increases exponentially. If each person who hears a rumor repeats it to two people per day, and if 20 people start the rumor, the number of people \(N\) who have heard the rumor after \(t\) days is given by $$ N(t)=20(3)^{t} $$ a) After what amount of time will 1000 people have heard the rumor? b) What is the doubling time for the number of people who have heard the rumor?

Use a calculator to find each of the following to four decimal places. $$\log 2$$

For pair of functions, find (a) \((f \circ g)(1)\) (b) \((g \circ f)(1) ;(\mathbf{c})(f \circ g)(x) ;(\mathbf{d})(g \circ f)(x)\). \(f(x)=x^{2}+4 ; g(x)=\sqrt{x-1}\)

The Richter scale, developed in \(1935,\) has been used for years to measure earthquake magnitude. The Richter magnitude \(m\) of an earthquake is given by $$ m=\log \frac{A}{A_{0}} $$ where \(A\) is the maximum amplitude of the earthquake and \(A_{0}\) is a constant. What is the magnitude on the Richter scale of an earthquake with an amplitude that is a million times \(A_{0} ?\)

The number of bacteria in a culture grows at an exponential growth rate of \(139 \%\) per hour. What is the doubling time for these bacteria?

The number of computers infected by a virus \(t\) days after it first appears usually increases exponentially. In 2009 the "Conflicker" worm spread from about 2.4 million computers on January 12 to about 3.2 million computers on January \(13 .\) Data: PC World a) Find the exponential growth rate \(k\) and write an equation for an exponential function that can be used to predict the number of computers infected \(t\) days after January \(12,2009\) b) Assuming exponential growth, estimate how long it took the Conflicker worm to infect 10 million computers.

Use a calculator to find each of the following to four decimal places. $$ e^{-2.64} $$

The concentration of acetaminophen in the body decreases exponentially after a dosage is given. In one clinical study, adult subjects averaged 11 micrograms \(/\) milliliter \((\mathrm{mcg} / \mathrm{mL})\) of the drug in their blood plasma 1 hr after a 1000 -mg dosage and 2 micrograms / milliliter 6 hr after dosage. Data: tylenolprofessional.com; Mark Knopp, M.D. a) Find the value \(k,\) and write an equation for an exponential function that can be used to predict the concentration of acetaminophen, in micrograms / milliliter, t hours after a 1000 -mg dosage. b) Estimate the concentration of acetaminophen 3 hr after a 1000 -mg dosage. c) To relieve a fever, the concentration of acetaminophen should go no lower than \(4 \mathrm{mcg} / \mathrm{mL}\). After how many hours will a 1000 -mg dosage drop to that level? d) Find the half-life of acetaminophen.