Assume the carrying capacity of the earth is

15

billion. Use the 1960s peak annual growth rate of

2.1​%

and population of

3

billion to predict the base growth rate and current growth rate with a logistic model. Assume a current population of

6.8

billion. How does the predicted growth rate compare to the actual growth rate of about

1.2​%

per​ year?

What is the base growth​ rate?

Assume the carrying capacity of the earth is

15

billion. Use the 1960s peak annual growth rate of

2.1​%

and population of

3

billion to predict the base growth rate and current growth rate with a logistic model. Assume a current population of

6.8

billion. How does the predicted growth rate compare to the actual growth rate of about

1.2​%

per​ year?

What is the base growth​ rate?

Assume the carrying capacity of the earth is

15

billion. Use the 1960s peak annual growth rate of

2.1​%

and population of

3

billion to predict the base growth rate and current growth rate with a logistic model. Assume a current population of

6.8

billion. How does the predicted growth rate compare to the actual growth rate of about

1.2​%

per​ year?

What is the base growth​ rate?

Assume the carrying capacity of the earth is

15

billion. Use the 1960s peak annual growth rate of

2.1​%

and population of

3

billion to predict the base growth rate and current growth rate with a logistic model. Assume a current population of

6.8

billion. How does the predicted growth rate compare to the actual growth rate of about

1.2​%

per​ year?

What is the base growth​ rate?

Assume the carrying capacity of the earth is

15

billion. Use the 1960s peak annual growth rate of

2.1​%

and population of

3

billion to predict the base growth rate and current growth rate with a logistic model. Assume a current population of

6.8

billion. How does the predicted growth rate compare to the actual growth rate of about

1.2​%

per​ year?

What is the base growth​ rate?

Assume the carrying capacity of the earth is

15

billion. Use the 1960s peak annual growth rate of

2.1​%

and population of

3

billion to predict the base growth rate and current growth rate with a logistic model. Assume a current population of

6.8

billion. How does the predicted growth rate compare to the actual growth rate of about

1.2​%

per​ year?

What is the base growth​ rate?

Assume the carrying capacity of the earth is

15

billion. Use the 1960s peak annual growth rate of

2.1​%

and population of

3

billion to predict the base growth rate and current growth rate with a logistic model. Assume a current population of

6.8

billion. How does the predicted growth rate compare to the actual growth rate of about

1.2​%

per​ year?

What is the base growth​ rate?

Assume you have a balance of ​$1400 on a credit card with an APR of 18​%, or 1.5​% per month. You start making monthly payments of​ $200, but at the same time you charge an additional ​$ 60 per month to the credit card.

Assume that interest for a given month is based on the balance for the previous month.

The following table shows how you can calculate your monthly balance. Complete and extend the table to show the balance at the end of each month until the debt is paid off. How long does it take to pay off the credit card​ debt?

Fill out the table row by​ row, and continue until the last full payment. ​(Round to the nearest cent as​ needed.)

Month Payment    Expenses Interest    New Balance

0 ​- ​-        ​ -    ​$ 1400

1    ​$200       ​$60      ​$ 1400 −​$200 plus +​$ 60 +​$ 21.00 =​$ 1281.00   2    ​$200       ​$60   ​    $ ?

A probability density function on R is a function f :R -> R satisfying (i) f(x)≥0 or all x e R and (ii) \int_(-\infty )^(\infty ) f(x)dx = 1. For which value(s) of k e R is the function

f(x)= e^(-x^(2))\root(3)(k^(5)) a probability density function? Explain.

Let X = ( X1, X2, X3, ,,,, Xn ) is iid,

f(x, a, b) = 1/ab * (x/a)^{(1-b)/b} 0 <= x <= a ,,,,, b < 1

then, find a two dimensional sufficient statistic for (a, b)

Suppose that you pick a bit string from the set of all bit strings of length ten. Find the probability that

1. the bit string has exactly two 1s;
2. the bit string begins and ends with 0;
3. the bit string has the sum of its digits equal to seven;
4. the bit string has more 0s than 1s;
5. the bit string has exactly two 1s, given that the string begins with a 1.

Given a complicated lim x → af (x), how do you quickly determine which items are

significant and which items are negligible —¿ quick guess in 5 seconds? Degree (or order) of largeness. How to convert your QuickGuess to an air tight high quality argument?

Problem 3Consider the following definitions for sets of characters:•Digits ={0,1,2,3,4,5,6,7,8,9}•Letters ={a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z}•Special characters ={∗,&,$,#}Compute the number of passwords that satisfy the given constraints

.(i) Strings of length 7. Characters can be special characters, digits, or letters ,with no repeated characters

.(ii) Strings of length 6. Characters can be special characters, digits, or letters ,with no repeated characters. The first character can not be a special char-acter.

Determine whether the following two planes x + 4y − z = 7 and 5x − 3y −7z = 11 are parallel, orthogonal, coincident (that is, the same) or none of these.

please show full working for learning purposes

Use the technique developed in this section to solve the minimization problem.

The minimum is C =

at (x, y, z) = .

find the general solution of the given differential equation

1. 2y''+3y'+y=t^2 +3sint

find the solution of the given initial value problem

1. y''−2y'−3y=3te^2t, y(0) =1, y'(0) =0

2.  y''−2y'+y=te^t +4, y(0) =1, y'(0) =1

Let S1 be the level surface given by the equation f(x,y,z) =k1and letS2be the level surface given by the equation g(x,y,z) =k2. Suppose that C is the curve of intersection of the surfacesS1andS2andassume that P is a point on C. show that any tangent vector to C at P must be parallel to∇f(P)×∇g(P)

Solve each of the following linear systems by the method of the example on page 283.

(a) 3x − y = 4        x + 5y = 9

(b) x − 2y + z = 1       y + z = 0         −x + y + z =−3

HInt; first find the QR decomposition of the coefficient matrix via the Gram–Schmidt process

Use ten iterations of the appropriate MATLAB function, with x^(0)=[0,...,0]', to solve Ax=b (approximately).

A)use Jacobi iteration.

B) use Gauss-siedel iteration.

1) make sure to use SOR with w=1.25, w=1.5, w=1.75,w=1.9, and optimal value if given.

* A=[1,-2,0,0;-2,5,-1,0;0,-1,2,-0.5;0,0,-0.5,1.25]] , B=[-3;5;2;3.5]. , (optimal w is 1.5431.)