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mathematics
calculus with applications
Calculus For Business, Economics And The Social And Life Sciences 11th Brief Edition Laurence Hoffmann, Gerald Bradley, David Sobecki, Michael Price - Solutions
If log10 x = −3, what is ln x?
It is estimated that the population of a certain country grows exponentially. If the population was 60 million in 1997 and 90 million in 2002, what will the population be in 2012?
In Exercises 39 through 46, find the largest and smallest values of the given function over the prescribed closed, bounded interval.F(x) = ex2−2x for 0 ≤ x ≤ 2
In Exercises 5 through 20, determine where the given function is increasing and decreasing and where its graph is concave upward and concave downward. Sketch the graph of the function. Show as many key features as possible (high and low points, points of inflection, vertical and horizontal
If log5(2x) = 7, what is ln x?
In Exercises 39 through 42, find the effective interest rate re for the given investment.Annual interest rate 6%, compounded quarterly
In Exercises 39 through 42, find the largest and smallest values of the given function over the prescribed closed, bounded interval.f(x) = ln(4x = x2) for 1 ≤ x ≤ 3
If log3(x − 5) = 2, what is ln x?
In Exercises 5 through 20, determine where the given function is increasing and decreasing and where its graph is concave upward and concave downward. Sketch the graph of the function. Show as many key features as possible (high and low points, points of inflection, vertical and horizontal
In Exercises 3 through 8, evaluate the given expression using properties of the natural logarithm. e³ Ve In- e¹/3
In Exercises 39 through 42, find the effective interest rate re for the given investment.Annual interest rate 8%, compounded daily (use k = 365)
In Exercises 1 through 38, differentiate the given function.f(x) = ex2 + 2x − 1
In Exercises 1 through 38, differentiate the given function.f(x) = (x2 + 3x + 5)e6x
Find the present value of $8,000 payable 10 years from now if the annual interest rate is 6.25% and interest is compounded:a. Semiannuallyb. Continuously
In Exercises 7 through 14, find all real numbers x that satisfy the given equation.8 = 2e0.04x
In Exercises 1 through 38, differentiate the given function. f(x) = V1 + et
In Exercises 3 through 8, evaluate the given expression using properties of the natural logarithm.e3 ln 2−2 ln 5
In Exercises 5 through 12, evaluate the given expressions. a. 5² b. T T 4/3
In Exercises 5 through 12, evaluate the given expressions.a. (23 − 32)11/7 b. (272/3 + 84/3)−3/2
In Exercises 1 through 38, differentiate the given function.f(x) = xe−x2
In Exercises 7 through 14, find all real numbers x that satisfy the given equation.5 = 1 + 4e−6x
In Exercises 5 through 20, determine where the given function is increasing and decreasing and where its graph is concave upward and concave downward. Sketch the graph of the function. Show as many key features as possible (high and low points, points of inflection, vertical and horizontal
In Exercises 5 through 12, evaluate the given expressions.a. (33)(3−2) b. (42/3)(22/3)
In Exercises 21 through 36, solve the given equation for x. 1/1/20 = = -1.2x Que
In a classic paper on the theory of conflict,* L. F. Richardson claimed that the proportion p of a population advocating war or other aggressive action at a time t satisfieswhere k and C are positive constants. Speculative day-trading in the stock market can be regarded as aggressive action.
In Exercises 1 through 38, differentiate the given function. h(t) e + t In t
In Exercises 1 through 38, differentiate the given function.f(x) = (1 − 3ex)2
In Exercises 15 through 30, find the derivative dy/dx. In some of these problems, you may need to use implicit differentiation or logarithmic differentiation. y = In e3x 1 + x
In Exercises 19 through 28, find all real numbers x that satisfy the given equation. 10 1-2²2² = 1,000
In Exercises 9 through 12, use logarithmic rules to rewrite each expression in terms of log3 2 and log3 5.log3 270
In Exercises 7 through 14, find all real numbers x that satisfy the given equation.4 ln x = 8
In Exercises 7 through 14, find all real numbers x that satisfy the given equation.5x = e3
In Exercises 1 through 38, differentiate the given function. f(x) = et + e 2 X
In Exercises 19 through 28, find all real numbers x that satisfy the given equation. 110 8 x-1 23-2²
In Exercises 15 through 30, find the derivative dy/dx. In some of these problems, you may need to use implicit differentiation or logarithmic differentiation. y 3 (x² + €²1)³e-2x 2,2/3 (1 + x - x²)²/3
In Exercises 9 through 12, use logarithmic rules to rewrite each expression in terms of log3 2 and log3 5.log3(2.5)
Paul Edwards owns an electronics firm. He determines that when he employs x thousand people, the profit will be P million dollars, whereHow many workers should Paul employ to maximize profit? What is the maximum profit? P(x) = ln(4x + 1) + 3x - x²
In Exercises 19 through 28, find all real numbers x that satisfy the given equation. 1-3x² = 34x
When professors select texts for their courses, they usually choose from among the books already on their shelves. For this reason, most publishers send complimentary copies of new texts to professors teaching related courses. The mathematics editor at a major publishing house estimates that if x
Devi Singh is an efficiency expert working for a major industrial firm. She determines that the daily output of a worker who has been on the job for t weeks is given by a function of the form Q(t) = 40 − Ae−kt. Devi observes that a typical worker produces 20 units a day initially and after 1
In Exercises 1 through 38, differentiate the given function. h(x) = 이외 e X 2
In Exercises 19 through 28, find all real numbers x that satisfy the given equation.10x2−1 = 103
In Exercises 21 through 36, solve the given equation for x. -In x = 50 + C
In Exercises 21 through 36, solve the given equation for x.3 = 2 + 5e−4x
In Exercises 15 through 30, find the derivative dy/dx. In some of these problems, you may need to use implicit differentiation or logarithmic differentiation.yex−x2= x + y
In Exercises 1 through 38, differentiate the given function.g(u) = ln(u2 − 1)3
In Exercises 1 through 38, differentiate the given function. f(t) = √Int + t Vlnt
The economics editor at a major publishing house estimates that if x thousand complimentary copies are distributed to professors, the first-year sales of a certain new text will be f(x) = 15 − 20e−0.3x thousand copies. Currently, the editor is planning to distribute 9,000 complimentary
In Exercises 21 through 36, solve the given equation for x.−2 ln x = b
In Exercises 15 through 30, find the derivative dy/dx. In some of these problems, you may need to use implicit differentiation or logarithmic differentiation.xe−y + ye−x = 3
In Exercises 29 through 32, use a graphing calculator to sketch the graph of the given exponential function.y = 31−x
In Exercises 15 through 30, find the derivative dy/dx. In some of these problems, you may need to use implicit differentiation or logarithmic differentiation. У - -Х e x + ln x
When a certain industrial machine has become t years old, its resale value will be V(t) = 4,800e−t/5 + 400 dollars.a. Sketch the graph of V(t). What happens to the value of the machine as t increases without bound?b. How much is the machine worth when it is new?c. How much will the machine be
In Exercises 5 through 12, evaluate the given expressions. a. (3¹-2)(327) 34.1 b. (16)* (125)-26 1/4(125-2/3 81, 8
A toxin is introduced into a bacterial colony, and t hours later, the population is given bya. What was the population when the toxin was introduced?b. When is the population maximized? What is the maximum population?c. What happens to the population in the long run (as t → + ∞)?
In Exercises 19 through 28, find all real numbers x that satisfy the given equation.(2.14)x−1 = (2.14)1−x
In Exercises 5 through 20, determine where the given function is increasing and decreasing and where its graph is concave upward and concave downward. Sketch the graph of the function. Show as many key features as possible (high and low points, points of inflection, vertical and horizontal
In Exercises 21 through 36, solve the given equation for x.32x−1 = 17
In Exercises 15 through 30, find the derivative dy/dx. In some of these problems, you may need to use implicit differentiation or logarithmic differentiation.y = (1 + e−x)4/5
An archaeological artifact is found to have 45% of its original 14C. How old is the artifact? (Use 5,730 years as the half-life of 14C.)
In Exercises 1 through 38, differentiate the given function.F(x) = ln(2x3 − 5x + 1)
In Exercises 5 through 20, determine where the given function is increasing and decreasing and where its graph is concave upward and concave downward. Sketch the graph of the function. Show as many key features as possible (high and low points, points of inflection, vertical and horizontal
In Exercises 19 through 28, find all real numbers x that satisfy the given equation.(3.2)2x−3 = (3.2)2−x
In Exercises 21 through 36, solve the given equation for x.2 = e0.06x
In Exercises 5 through 20, determine where the given function is increasing and decreasing and where its graph is concave upward and concave downward. Sketch the graph of the function. Show as many key features as possible (high and low points, points of inflection, vertical and horizontal
In Exercises 5 through 12, evaluate the given expressions.a. (32)5/2 b. (e2e3/2)4/3
In Exercises 9 through 12, use logarithmic rules to rewrite each expression in terms of log3 2 and log3 5. 64 log:(195)
In Exercises 1 through 38, differentiate the given function.f(x) = e√3x
In Exercises 7 through 14, find all real numbers x that satisfy the given equation.log9(4x − 1) = 2
In Exercises 13 through 18, use the properties of exponents to simplify the given expressions. a. (x + y)⁰ (x²y³) 1/6 b. (x¹¹²)(x² + y²0
In Exercises 9 through 12, use logarithmic rules to rewrite each expression in terms of log3 2 and log3 5.log3 100
In Exercises 1 through 38, differentiate the given function.f(x) = e1/x
In Exercises 5 through 20, determine where the given function is increasing and decreasing and where its graph is concave upward and concave downward. Sketch the graph of the function. Show as many key features as possible (high and low points, points of inflection, vertical and horizontal
In Exercises 7 through 14, find all real numbers x that satisfy the given equation.ln(x − 2) + 3 = ln(x + 1)
In Exercises 13 through 18, use the properties of exponents to simplify the given expressions.a. (27x6)2/3 b. (8x2y3)1/3
In Exercises 5 through 20, determine where the given function is increasing and decreasing and where its graph is concave upward and concave downward. Sketch the graph of the function. Show as many key features as possible (high and low points, points of inflection, vertical and horizontal
In Exercises 1 through 38, differentiate the given function.f(x) = ln x3
In Exercises 5 through 20, determine where the given function is increasing and decreasing and where its graph is concave upward and concave downward. Sketch the graph of the function. Show as many key features as possible (high and low points, points of inflection, vertical and horizontal
In Exercises 13 through 20, use logarithmic rules to simplify each expression. In x²- X
In Exercises 7 through 14, find all real numbers x that satisfy the given equation.e2x + ex − 2 = 0
In Exercises 13 through 20, use logarithmic rules to simplify each expression. In(x² √4 - x²)
In Exercises 13 through 20, use logarithmic rules to simplify each expression.log2(x4y3)
In Exercises 13 through 18, use the properties of exponents to simplify the given expressions.a. (x1/3)3/2 b. (x2/3)−3/4
In Exercises 1 through 38, differentiate the given function. x7²A = (x)ƒ£
In Exercises 1 through 38, differentiate the given function.f(x) = ln 2x
In Exercises 7 through 14, find all real numbers x that satisfy the given equation.e2x + 2ex − 3 = 0
In Exercises 13 through 20, use logarithmic rules to simplify each expression.log3(x5y−2)
In Exercises 1 through 38, differentiate the given function.f(x) = x2 ln x
In Exercises 15 through 30, find the derivative dy/dx. In some of these problems, you may need to use implicit differentiation or logarithmic differentiation.y = x2e−x
In Exercises 13 through 20, use logarithmic rules to simplify each expression. In x²(3 - x)²/3 √x² + x + 1]
In Exercises 13 through 18, use the properties of exponents to simplify the given expressions. a. (x²y3z)³ b. ( 4 -21/6
In Exercises 13 through 18, use the properties of exponents to simplify the given expressions.a. (−2t−3)(3t2/3) b. (t−2/3)(t3/4)
In Exercises 13 through 20, use logarithmic rules to simplify each expression. In + Xx X
In Exercises 1 through 38, differentiate the given function. f(x) = In x X
In Exercises 1 through 38, differentiate the given function.f(x) = x ln √x
In Exercises 1 through 38, differentiate the given function. f(x) = In x + 1 x-1,
In Exercises 15 through 30, find the derivative dy/dx. In some of these problems, you may need to use implicit differentiation or logarithmic differentiation. y = ln Vx² + 4x + 1
In Exercises 15 through 30, find the derivative dy/dx. In some of these problems, you may need to use implicit differentiation or logarithmic differentiation.y = 2e3x + 5
In Exercises 5 through 20, determine where the given function is increasing and decreasing and where its graph is concave upward and concave downward. Sketch the graph of the function. Show as many key features as possible (high and low points, points of inflection, vertical and horizontal
In Exercises 13 through 18, use the properties of exponents to simplify the given expressions.a. (t5/6)−6/5 b. (t−3/2)−2/3
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