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Concept explainers
Biomass Biomass is a measure of the amount of living matter in an ecosystem. The biomass s(t) in a given ecosystem increases at a rate of about 3.5 tons per year and decreases by about 1.9% per year. This situation can be modeled by the
(a) Find the general solution of the differential equation.
(b) Use a graphing utility to graph the slope field for the differential equation. What do you notice?
(c) Explain what happens to the biomass as
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Chapter 6 Solutions
Bundle: Calculus: Early Transcendental Functions, 7th + Webassign, Multi-term Printed Access Card
- 3. f(7) 3. Find the domain of each of the following functions. 1 1. f(x)=2-6x+8 2. f(x)=√√7-x 4. A manufacturer has a monthly fixed cost of $40,000 and a production cost of $8 for each unit produced. The product sells for $12 per unit.arrow_forward7. Evaluate the following limits and justify each step. (a) lim (3x²+2x+1) 1 x²+4x-12 (b) lim 1 2 x² - 2x t-√√3t+4 (c) lim t-0 4-t x²-6x+5 (d) lim (e) lim x 5 x-5 x→2 x²+2x+3 4u+1-3 (f) lim u➡2 u-2 1 (g) lim x-3 2 x 55 x - 7x4 +4 (h) lim xx 5x+2x-1 x+1 (i) lim x²-2x+5 - 7x8+4x7 +5xarrow_forward6. Given the following graph f(x). (-2,2) 2- -5 -3 -2 (-2,-1) -1 (0,1) -2- 1 (3,0) 2 3 4 5 (3,-1) א X Compute each of the following. (a) f(-2) (b) lim f(x) #129 (c) lim f(x) *→12+ (d) lim f(x) 811H (e) f(0) (f) lim f(x) 8011 (m) Is the function continuous at x = -2,0,3? Why or why not? (g) lim f(x) +0x (h) lim f(x) x 0 (i) f(3) (j) lim f(x) x-3- (k) lim f(x) x+3+ (1) lim f(x) #13arrow_forward
- 3. Compute the profit corresponding to 12,000 units. 5. A rectangular box is to have a square base and a volume of 20 ft3. The material for the base costs $0.30 per ft2, the material for the sides cost $0.10 per ft2, and the material for the top costs $0.20 per ft2. Letting a denote the length of one side of the base, find a function in the variable x giving the cost of constructing the box. 6. Given the following graph f(x).arrow_forward8. On what intervals, each function continuous? (a) f(x) = 3x11 + 4x²+1 3x²+5x-1 (b) g(x) = x²-4 X, x < 1, QTs the function f(x) continuous at = 1? Use the definition of continuity to justifyarrow_forwardreview problem please help!arrow_forward
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
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