Composition of Functions and Modeling — Unit test Answers

Which inequality is equivalent to ?

You can use a system of equations to graph and solve the polynomial equation . Which statement is true?

Two different radioactive isotopes decay to 10% of their respective original amounts. Isotope A does this in 33 days, while isotope B does this in 43 days. What is the approximate difference in the half-lives of the isotopes?

Which graph shows the solution set of ?

The magnitude, M, of an earthquake is defined to be , where I is the intensity of the earthquake (measured by the amplitude of the seismograph wave) and S is the intensity of a “standard” earthquake, which is barely detectable. What is the magnitude of an earthquake that is 1,000 times more intense than a standard earthquake? Use a calculator. Round your answer to the nearest tenth.

What is the solution of ?

What are the roots of the polynomial equation ? Use a graphing calculator and a system of equations.

One brand of vinegar has a pH of 4.5. Another brand has a pH of 5.0. The equation for the pH of a substance is pH = –log[H+], where H+ is the concentration of hydrogen ions. What is the approximate difference in the concentration of hydrogen ions between the two brands of vinegar?

What is the solution to 4x 3 – 3x 2 – 7x < 0?

Which equation has x = 4 as the solution?

The intensity, or loudness, of a sound can be measured in decibels (dB), according to the equation , where I is the intensity of a given sound and I0 is the threshold of hearing intensity. What is the intensity, in decibels, [I(dB)], when ?

Which expression is equivalent to ?

Regular exercise can help a person lower their resting heart rate. Suppose an individual’s resting heart rate, in beats per minute, is modeled by the function f(x) = –0.1x 3 + 0.6x 2 + 85 after x weeks of regular exercise.How many weeks of exercise are necessary to lower the individual’s resting heart rate below 70 beats per minute?

What is rewritten using the power property?