Calculus For The Life Sciences
2nd Edition
ISBN: 9780321964038
Author: GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher: Pearson Addison Wesley,
expand_more
expand_more
format_list_bulleted
Question
Chapter 13.1, Problem 14E
To determine
To find:
The value of
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Question 1. (10 points)
A researcher is studying tumours in mice. The growth rate for the volume of the tumour V(t) in cm³ is given by
dV
=
1.45V(2 In(V+1)).
dt
(a) (4 pts) Find all the equilibria and determine their stability using the stability condition.
(b) (2 pts) Draw the phase plot f(V) versus V where f(V) = V'. You may find it helpful to use Desmos or Wolfram Alpha to plot the graph of
f(V) versus V (both are free to use online), or you can plot it by hand if you like. On the plot identify each equilibrium as stable or unstable.
(c) (4 pts) Draw direction arrows for the case where the tumour starts at size 3cm³ and for the case where the tumour starts at size 9cm³. Explain
in biological terms what happens to the size of each of these tumours at time progresses.
For the system consisting of the two planes:plane 1: -x + y + z = 0plane 2: 3x + y + 3z = 0a) Are the planes parallel and/or coincident? Justify your answer. What does this tell you about the solution to the system?b) Solve the system (if possible). Show a complete solution. If there is a line of intersection express it in parametric form.
Question 2: (10 points) Evaluate the definite integral.
Use the following form of the definition of the integral to evaluate the integral:
Theorem: Iff is integrable on [a, b], then
where Ax = (ba)/n and x₂ = a + i^x.
You might need the following formulas.
IM³
L² (3x²
(3x²+2x-
2x - 1)dx.
n
[f(z)dz lim f(x)Az
a
n→∞
i=1
n(n + 1)
2
n
i=1
n(n+1)(2n+1)
6
Chapter 13 Solutions
Calculus For The Life Sciences
Ch. 13.1 - Repeat Example 1a for the function f(x)=2x2 on...Ch. 13.1 - Prob. 2YTCh. 13.1 - Prob. 3YTCh. 13.1 - Prob. 1ECh. 13.1 - Prob. 2ECh. 13.1 - Prob. 3ECh. 13.1 - Prob. 4ECh. 13.1 - Prob. 5ECh. 13.1 - Prob. 6ECh. 13.1 - Prob. 7E
Ch. 13.1 - Prob. 8ECh. 13.1 - Prob. 9ECh. 13.1 - Prob. 10ECh. 13.1 - Prob. 11ECh. 13.1 - Prob. 12ECh. 13.1 - Prob. 13ECh. 13.1 - Prob. 14ECh. 13.1 - Prob. 15ECh. 13.1 - Prob. 16ECh. 13.1 - Prob. 17ECh. 13.1 - Prob. 18ECh. 13.1 - Prob. 19ECh. 13.1 - Prob. 20ECh. 13.1 - Prob. 21ECh. 13.1 - Prob. 22ECh. 13.1 - Find the cumulative distribution function for the...Ch. 13.1 - Prob. 24ECh. 13.1 - Prob. 25ECh. 13.1 - Prob. 26ECh. 13.1 - Prob. 27ECh. 13.1 - Prob. 28ECh. 13.1 - Show that each function defined as follows is a...Ch. 13.1 - Prob. 30ECh. 13.1 - Show that each function defined as follows is a...Ch. 13.1 - Prob. 32ECh. 13.1 - Prob. 33ECh. 13.1 - Prob. 34ECh. 13.1 - Prob. 35ECh. 13.1 - Prob. 36ECh. 13.1 - Prob. 45ECh. 13.1 - Prob. 47ECh. 13.1 - Prob. 48ECh. 13.1 - Prob. 49ECh. 13.2 - YOUR TURN 1 Repeat Example 1 for the probability...Ch. 13.2 - Prob. 2YTCh. 13.2 - Prob. 3YTCh. 13.2 - In Exercises 1-8, a probability density function...Ch. 13.2 - Prob. 2ECh. 13.2 - Prob. 3ECh. 13.2 - Prob. 4ECh. 13.2 - Prob. 5ECh. 13.2 - Prob. 6ECh. 13.2 - Prob. 7ECh. 13.2 - Prob. 8ECh. 13.2 - Prob. 9ECh. 13.2 - Prob. 10ECh. 13.2 - Prob. 11ECh. 13.2 - Prob. 12ECh. 13.2 - Prob. 13ECh. 13.2 - Prob. 14ECh. 13.2 - Prob. 15ECh. 13.2 - Prob. 16ECh. 13.2 - Prob. 17ECh. 13.2 - Prob. 18ECh. 13.2 - Prob. 19ECh. 13.2 - Prob. 20ECh. 13.2 - Prob. 21ECh. 13.2 - Prob. 22ECh. 13.2 - Prob. 23ECh. 13.2 - Prob. 24ECh. 13.2 - Length of a leaf The length of a leaf on a tree is...Ch. 13.2 - Prob. 26ECh. 13.2 - Prob. 30ECh. 13.2 - Prob. 31ECh. 13.2 - Prob. 33ECh. 13.2 - Prob. 34ECh. 13.2 - Prob. 35ECh. 13.2 - Prob. 36ECh. 13.2 - Prob. 37ECh. 13.2 - Prob. 39ECh. 13.2 - Prob. 40ECh. 13.3 - YOUR TURN Repeat Example 2 for a flashlight...Ch. 13.3 - Prob. 1ECh. 13.3 - Prob. 2ECh. 13.3 - Prob. 3ECh. 13.3 - Prob. 4ECh. 13.3 - Prob. 5ECh. 13.3 - Prob. 6ECh. 13.3 - Prob. 7ECh. 13.3 - Prob. 8ECh. 13.3 - Prob. 9ECh. 13.3 - Prob. 10ECh. 13.3 - Prob. 11ECh. 13.3 - Prob. 12ECh. 13.3 - Prob. 13ECh. 13.3 - Prob. 14ECh. 13.3 - Describe the standard normal distribution. What...Ch. 13.3 - Prob. 16ECh. 13.3 - Suppose a random variable X has the Poisson...Ch. 13.3 - Prob. 19ECh. 13.3 - Prob. 20ECh. 13.3 - Prob. 21ECh. 13.3 - Prob. 22ECh. 13.3 - Prob. 23ECh. 13.3 - Find each of the following probabilities for the...Ch. 13.3 - Prob. 25ECh. 13.3 - Prob. 26ECh. 13.3 - Prob. 27ECh. 13.3 - Prob. 28ECh. 13.3 - Prob. 30ECh. 13.3 - Determine the cumulative distribution function for...Ch. 13.3 - Prob. 36ECh. 13.3 - Prob. 37ECh. 13.3 - Prob. 38ECh. 13.3 - Prob. 39ECh. 13.3 - Pygmy Height The average height of a member of a...Ch. 13.3 - Prob. 41ECh. 13.3 - Prob. 42ECh. 13.3 - Prob. 43ECh. 13.3 - Prob. 44ECh. 13.3 - Prob. 45ECh. 13.3 - Prob. 46ECh. 13.3 - Prob. 47ECh. 13.3 - Prob. 48ECh. 13.3 - Prob. 49ECh. 13.3 - Earthquakes The proportion of the times in days...Ch. 13.3 - Prob. 51ECh. 13.3 - Prob. 52ECh. 13.3 - Prob. 53ECh. 13.3 - Prob. 54ECh. 13.3 - Prob. 55ECh. 13.3 - Printer Failure The lifetime of a printer costing...Ch. 13.3 - Electronic Device The time to failure of a...Ch. 13.CR - Prob. 1CRCh. 13.CR - Prob. 3CRCh. 13.CR - Prob. 4CRCh. 13.CR - Prob. 5CRCh. 13.CR - Prob. 6CRCh. 13.CR - Prob. 7CRCh. 13.CR - Prob. 8CRCh. 13.CR - Prob. 9CRCh. 13.CR - Prob. 10CRCh. 13.CR - Prob. 11CRCh. 13.CR - Prob. 12CRCh. 13.CR - Prob. 13CRCh. 13.CR - Prob. 14CRCh. 13.CR - Prob. 15CRCh. 13.CR - Prob. 16CRCh. 13.CR - Prob. 17CRCh. 13.CR - Prob. 18CRCh. 13.CR - Prob. 19CRCh. 13.CR - Prob. 20CRCh. 13.CR - Prob. 21CRCh. 13.CR - Prob. 22CRCh. 13.CR - Prob. 23CRCh. 13.CR - Prob. 24CRCh. 13.CR - Prob. 25CRCh. 13.CR - Prob. 26CRCh. 13.CR - Prob. 27CRCh. 13.CR - Prob. 28CRCh. 13.CR - Prob. 29CRCh. 13.CR - Prob. 30CRCh. 13.CR - Prob. 31CRCh. 13.CR - Prob. 32CRCh. 13.CR - Prob. 33CRCh. 13.CR - Prob. 34CRCh. 13.CR - Prob. 35CRCh. 13.CR - Prob. 36CRCh. 13.CR - Prob. 39CRCh. 13.CR - Prob. 40CRCh. 13.CR - Prob. 41CRCh. 13.CR - Prob. 42CRCh. 13.CR - Prob. 43CRCh. 13.CR - Prob. 44CRCh. 13.CR - Prob. 45CRCh. 13.CR - Prob. 46CRCh. 13.CR - Prob. 47CRCh. 13.CR - Prob. 48CRCh. 13.CR - Prob. 52CRCh. 13.CR - Prob. 54CRCh. 13.CR - Prob. 55CRCh. 13.CR - Prob. 56CRCh. 13.CR - Prob. 57CRCh. 13.CR - Prob. 58CRCh. 13.CR - Prob. 59CRCh. 13.CR - Prob. 60CRCh. 13.CR - Prob. 61CRCh. 13.CR - Yeast cells The famous statistician William...Ch. 13.CR - Prob. 65CRCh. 13.CR - Equipment Insurance A piece of equipment is being...
Knowledge Booster
Similar questions
- For the system consisting of the three planes:plane 1: -4x + 4y - 2z = -8plane 2: 2x + 2y + 4z = 20plane 3: -2x - 3y + z = -1a) Are any of the planes parallel and/or coincident? Justify your answer.b) Determine if the normals are coplanar. What does this tell you about the system?c) Solve the system if possible. Show a complete solution (do not use matrix operations). Classify the system using the terms: consistent, inconsistent, dependent and/or independent.arrow_forwardFor the system consisting of the three planes:plane 1: -4x + 4y - 2z = -8plane 2: 2x + 2y + 4z = 20plane 3: -2x - 3y + z = -1a) Are any of the planes parallel and/or coincident? Justify your answer.b) Determine if the normals are coplanar. What does this tell you about the system?c) Solve the system if possible. Show a complete solution (do not use matrix operations). Classify the system using the terms: consistent, inconsistent, dependent and/or independent.arrow_forwardOpen your tool box and find geometric methods, symmetries of even and odd functions and the evaluation theorem. Use these to calculate the following definite integrals. Note that you should not use Riemann sums for this problem. (a) (4 pts) (b) (2 pts) 3 S³ 0 3-x+9-dz x3 + sin(x) x4 + cos(x) dx (c) (4 pts) L 1-|x|dxarrow_forward
- An engineer is designing a pipeline which is supposed to connect two points P and S. The engineer decides to do it in three sections. The first section runs from point P to point Q, and costs $48 per mile to lay, the second section runs from point Q to point R and costs $54 per mile, the third runs from point R to point S and costs $44 per mile. Looking at the diagram below, you see that if you know the lengths marked x and y, then you know the positions of Q and R. Find the values of x and y which minimize the cost of the pipeline. Please show your answers to 4 decimal places. 2 Miles x = 1 Mile R 10 miles miles y = milesarrow_forwardAn open-top rectangular box is being constructed to hold a volume of 150 in³. The base of the box is made from a material costing 7 cents/in². The front of the box must be decorated, and will cost 11 cents/in². The remainder of the sides will cost 3 cents/in². Find the dimensions that will minimize the cost of constructing this box. Please show your answers to at least 4 decimal places. Front width: Depth: in. in. Height: in.arrow_forwardFind and classify the critical points of z = (x² – 8x) (y² – 6y). Local maximums: Local minimums: Saddle points: - For each classification, enter a list of ordered pairs (x, y) where the max/min/saddle occurs. Enter DNE if there are no points for a classification.arrow_forward
- Suppose that f(x, y, z) = (x − 2)² + (y – 2)² + (z − 2)² with 0 < x, y, z and x+y+z≤ 10. 1. The critical point of f(x, y, z) is at (a, b, c). Then a = b = C = 2. Absolute minimum of f(x, y, z) is and the absolute maximum isarrow_forwardThe spread of an infectious disease is often modeled using the following autonomous differential equation: dI - - BI(N − I) − MI, dt where I is the number of infected people, N is the total size of the population being modeled, ẞ is a constant determining the rate of transmission, and μ is the rate at which people recover from infection. Close a) (5 points) Suppose ẞ = 0.01, N = 1000, and µ = 2. Find all equilibria. b) (5 points) For the equilbria in part a), determine whether each is stable or unstable. c) (3 points) Suppose ƒ(I) = d. Draw a phase plot of f against I. (You can use Wolfram Alpha or Desmos to plot the function, or draw the dt function by hand.) Identify the equilibria as stable or unstable in the graph. d) (2 points) Explain the biological meaning of these equilibria being stable or unstable.arrow_forwardFind the indefinite integral. Check Answer: 7x 4 + 1x dxarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
