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mathematics
precalculus

Questions and Answers of Precalculus

In problem, convert each exponential statement to an equivalent statement involving a logarithm.a5 = m
In problem, determine whether the given function is linear, exponential, or neither. For those that are linear functions, find a linear function that models the data; for those that are exponential,
For 6% compounded continuouslyIn problem, find the effective rate of interest.
In problem, find the exact value of each logarithm without using a calculator.log2 1
In problem, find the inverse of each one-to-one function. State the domain and the range of each inverse function. Annual Rainfall (inches) Location Mt Waialeale, Hawaii 460.00 Monrovia, Liberia
In problem, solve each logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places.ln x + In(x + 2) = 4
In problem, find the domain of the composite function f ° g.f(x) = √x; g(x) = 2x + 3
In problem, convert each exponential statement to an equivalent statement involving a logarithm.52 = z
After the Challenger disaster in 1986, a study was made of the 23 launches that preceded the fatal flight. A mathematical model was developed involving the relationship between the Fahrenheit
In problem, determine whether the given function is linear, exponential, or neither. For those that are linear functions, find a linear function that models the data; for those that are exponential,
For 5% compounded continuouslyIn problem, find the effective rate of interest.
In problem, change each logarithmic statement to an equivalent statement involving an exponent.ln x = 4
In problem, solve each logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places.log5(x + 3) = 1 - 1og5(x - 1)
In problem, find the domain of the composite function f ° g. f(x) 8(x) x + 3'
In problem, f(x) = 3x and g(x) = log3 x. Evaluate:(a) f(1)(b) g(81)(c) f(-4)(d) g(1/243)
Often environmentalists capture an endangered species and transport the species to a controlled environment where the species can produce offspring and regenerate its population.Suppose that six
In problem, the graph of a function f is given. Use the horizontal-line test to determine whether f is one-to-one. y -3 3х
For 6% compounded monthlyIn problem, find the effective rate of interest.
In problem, approximate each number using a calculator. Express your answer rounded to three decimal places.e2.1
In problem, change each logarithmic statement to an equivalent statement involving an exponent.ln 4 = x
In problem, solve each logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places.log8(x + 6) = 1 – log8(x + 4)
In problem, find the domain of the composite function f ° g. 4 g(x) X – 1' %3D f(x)
In problem, f(x) = 3x and g(x) = log3 x. Evaluate:(a) f(4)(b) g(9)(c) f(-2)(d) g(1/27)
In problem, the graph of a function f is given. Use the horizontal-line test to determine whether f is one-to-one. Ул 3 -3 3х
The logistic growth modelrepresents the population (in grams) of a bacterium after t hours.(a) Determine the carrying capacity of the environment.(b) What is the growth rate of the bacteria?(c)
For 5% compounded quarterlyIn problem, find the effective rate of interest.
In problem, approximate each number using a calculator. Express your answer rounded to three decimal places.e-0.85
In problem, change each logarithmic statement to an equivalent statement involving an exponent.log2 6 = x
In problem, solve each logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places.log6(x + 4) + log6(x + 3) = 1
In problem, find the domain of the composite function f Â° g. 2 8(x) f(x) = x + 3'
In problem, the graph of a function f is given. Use the horizontal-line test to determine whether f is one-to-one. y 2 -3 3 х
The hotel Bora-Bora is having a pig roast. At noon, the chef put the pig in a large earthen oven.The pig€™s original temperature was 75°F. At 2:00 PM the chef checked the
To get $800 after 2½ years at 8% compounded continuouslyIn problem, find the principal needed now to get each amount; that is, find the present value.
In problem, the function f is one-to-one. Find the inverse of each function and check your answer.f(x) = 1 + x1/3
In problem, approximate each number using a calculator. Express your answer rounded to three decimal places.e-1.3
In problem, change each logarithmic statement to an equivalent statement involving an exponent.log3 2 = x
In problem, solve each logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places.log2(x + 7) + log2(x + 8) = 1
In problem, find the domain of the composite function f ° g.
In problem, the graph of a function f is given. Use the horizontal-line test to determine whether f is one-to-one. y 3 3 х -3 -3F
To get $80 after 3¼ years at 9% compounded continuouslyIn problem, find the principal needed now to get each amount; that is, find the present value.
After the release of radioactive material into the atmosphere from a nuclear power plant at Chernobyl (Ukraine) in 1986, the hay in Austria was contaminated by iodine 131 (half-life 8 days). If it is
In problem, the function f is one-to-one. Find the inverse of each function and check your answer.f(x) = 3/x1/3
In problem, approximate each number using a calculator. Express your answer rounded to three decimal places.e1.2
In problem, change each logarithmic statement to an equivalent statement involving an exponent.logb 4 = 2
In problem, solve each logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places.log(2x) - log(x - 3) = 1
In problem, for the given functions and , find:(a) (f ° g)(4)(b) (g ° f)(2)(c) (f ° f)(1)(d) (g ° g)(0) 2 = x2; g(x) x + 1
In problem, the graph of a function f is given. Use the horizontal-line test to determine whether f is one-to-one. y . 3х -3 -3
To get $300 after 4 years at 3% compounded dailyIn problem, find the principal needed now to get each amount; that is, find the present value.
Salt (NaCl) decomposes in water into sodium (Na+) and chloride (Cl-) ions according to the law of uninhibited decay. If the initial amount of salt is 25 kilograms and, after 10 hours, 15 kilograms of
In problem, the function f is one-to-one. Find the inverse of each function and check your answer.f(x) = √x - 2
In problem, approximate each number using a calculator. Express your answer rounded to three decimal places.(a) 2.73.1(b) 2.713.14(c) 2.7183.141(d) eπ
In problem, change each logarithmic statement to an equivalent statement involving an exponent.loga 3 = 6
In problem, solve each logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places.log(2x + 1) = 1 + log(x - 2)
In problem, for the given functions and , find:(a) (f ° g)(4)(b) (g ° f)(2)(c) (f ° f)(1)(d) (g ° g)(0) 3 f(x) 8(x) = Vĩ x + 1'
In problem, the graph of a function f is given. Use the horizontal-line test to determine whether f is one-to-one. y. 3 x -3 -3
To get $600 after 2 years at4%compounded quarterlyIn problem, find the principal needed now to get each amount; that is, find the present value.
In problem, the function f is one-to-one. Find the inverse of each function and check your answer. f(x) = – 1
Reacting with water in an acidic solution at 35°C, sucrose (C12H22O11) decomposes into glucose (C6H12O6) and fructose (C6H12O6)* according to the law of uninhibited decay. An initial amount of 0.40
In problem, approximate each number using a calculator. Express your answer rounded to three decimal places.(a) 3.127(b) 3.142.71(c) 3.1412.718(d) πe
In problem, change each logarithmic statement to an equivalent statement involving an exponent.log3(1/9) = -2
In problem, solve each logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places.log x + log (x - 21) = 2
In problem, for the given functions and , find:(a) (f ° g)(4)(b) (g ° f)(2)(c) (f ° f)(1)(d) (g ° g)(0) 3 f(x) = |x – 2|; g(x) x* + 2 3.
To get $800 after 3 1/3 years at 7% compounded monthlyIn problem, find the principal needed now to get each amount; that is, find the present value.
In problem, the function f is one-to-one. Find the inverse of each function and check your answer. f(x) %3D 3 + x
In problem, determine whether the function is one-to-one.{(1, 2), (2, 8), (3, 18), (4, 32)}
In problem, approximate each number using a calculator. Express your answer rounded to three decimal places.(a) 22.7(b) 22.71(c) 22.718(d) 2e
At 45°C, dinitrogen pentoxide (N2O5) decomposes into nitrous dioxide (NO2) and oxygen (O2) according to the law of uninhibited decay. An initial amount of 0.25 M of dinitrogen pentoxide decomposes
In problem, change each logarithmic statement to an equivalent statement involving an exponent.log2 8 = 3
In problem, solve each logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places.log x + log(x + 15) = 2
In problem, for the given functions and , find:(a) (f ° g)(4)(b) (g ° f)(2)(c) (f ° f)(1)(d) (g ° g)(0) f(x) = |x|; g(x) 8(x) x + 1
To get $1000 after 2½ years at 6% compounded dailyIn problem, find the principal needed now to get each amount; that is, find the present value.
In problem, the function f is one-to-one. Find the inverse of each function and check your answer. 2х + 3 f(x) : 5х — 2
In problem, determine whether the function is one-to-one.{(0, 0), (1, 1), (2, 16), (3, 81)}
In problem, approximate each number using a calculator. Express your answer rounded to three decimal places.(a) 23.14(b) 23.141(c) 23.1415(d) 2π
Under certain water conditions, the free chlorine (hypochlorous acid, HOCl) in a swimming pool decomposes according to the law of uninhibited decay. After shocking his pool, Ben tested the water and
In problem, change each exponential statement to an equivalent statement involving a logarithm.e2.2 = M
In problem, solve each logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places.2 log3(x + 4) - 1og3 9 = 2
In problem, for the given functions and , find:(a) (f ° g)(4)(b) (g ° f)(2)(c) (f ° f)(1)(d) (g ° g)(0)f(x) = √x + 1; g(x) = 3x
To get $75 after 3 years at 8% compounded quarterlyIn problem, find the principal needed now to get each amount; that is, find the present value.
In problem, state why the graph of the function is one-to-one. Then draw the graph of the inverse function f-1. For convenience (and as a hint), the graph of y = x is also given. Ул У %3DX, У-х,
In problem, determine whether the function is one-to-one.{(-2, 5), (-1, 3), (3, 7), (4, 12)}
In problem, approximate each number using a calculator. Express your answer rounded to three decimal places.(a) 51.7(b) 51.73(c) 51.732(d) 5√3
A beer stein has a temperature of 28°F. It is placed in a room with a constant temperature of 70°F. After 10 minutes, the temperature of the stein has risen to 35°F. What will the temperature of
In problem, change each exponential statement to an equivalent statement involving a logarithm.ex = 8
In problem, solve each logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places.3 log2(x - 1) + log2 4 = 5
In problem, for the given functions and , find:(a) (f ° g)(4)(b) (g ° f)(2)(c) (f ° f)(1)(d) (g ° g)(0)f(x) = √x; g(x) = 2x
To get $100 after 2 years at 6% compounded monthlyIn problem, find the principal needed now to get each amount; that is, find the present value.
In problem, state why the graph of the function is one-to-one. Then draw the graph of the inverse function f-1. For convenience (and as a hint), the graph of y = x is also given. Ул у -хи (3, 3)
In problem, determine whether the function is one-to-one.{(2, 6), (-3, 6), (4, 9), (1, 10)}
In problem, approximate each number using a calculator. Express your answer rounded to three decimal places.(a) 32.2(b) 32.23(c) 32.236(d) 3√5
A thermometer reading 8°C is brought into a room with a constant temperature of 35°C. If the thermometer reads 15°C after 3 minutes, what will it read after being in the room for 5 minutes? For 10
A thermometer reading 72°F is placed in a refrigerator where the temperature is a constant 38°F.(a) If the thermometer reads 60°F after 2 minutes, what will it read after 7 minutes?(b) How long
In problem, change each exponential statement to an equivalent statement involving a logarithm.3x = 4.6
In problem, solve each logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places.2 log5 x = 3 log5 4
In problem, for the given functions and , find:(a) (f ° g)(4)(b) (g ° f)(2)(c) (f ° f)(1)(d) (g ° g)(0)f(x) = 2x2; g(x) = 1 - 3x2
$400 invested at 7% compounded continuously after a period of 3 yearsIn problem, find the amount that results from each investment.
In problem,(a) Verify that the function is one-to-one, and(b) Find the inverse of the given function.{( -1, 4), (0, 2), (1, 5), (3,7)}
In problem, determine whether the function is one-to-one. Domain Range Bob Karla Dave Debra John Phoebe Chuck
True or FalseThe graphs of y = 3x and y = (1/3)x are identical.
A pizza pan is removed at 5:00 PM from an oven whose temperature is fixed at 450°F into a room that is a constant 70°F. After 5 minutes, the pan is 300°F.(a) At what time is the

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