Search the internet for real-world applications of logarithms or exponential functions. Share the application you discovered with the class along with how it relates to logarithms or exponential functions. Besure to cite the resource. What is the relationship between exponentials and logarithms?

A company produces wooden chairs and tables. Each chair uses 10 lbs. of wood and takes 10 hours to construct. Each table uses 15 lbs. of wood and takes 5 hours to construct. There are up to 150 lbs. of wood available and up to 110 labor hours available. If the profit on each chair is $3 and the profit on each table is 4$. We wish to maximize the profit. Let x be the number of chairs produced and y be the number of tables produced.

1. What is the formula to be maximized?
2. Write down the set of linear inequalities associated with the situation. Note: You should recognize that x and y can’t be negative.
3. Graph the feasible region by hand.
4. Find the coordinates of each vertex of the feasible region
5. Use these vertices to find the associated maximum

For each counties in the metro area, it gives an estimate of the population on Jan. 1, 2000, and the percent change between 1/1/2000 and 1/1/2010. If we assume that the percent change for each county is constant, then the population of each county can be modeled using an exponential function with a growth rate given by the annual percentage change.

1. Find an exponential function of the form P(t)=P₀e^kt , which gives the population of the county in the year 2000 + t.
2. Evaluate the function at t = 16 and give a verbal interpretation of your answer.
3. Find the derivative of the function.
4. Evaluate the derivative at t = 16 and give a verbal interpretation of your answer.

Let l:ax1+bx2 =c be a line where a^2+b^2 =1.Find the map f: R^2 →R^2 that represents the reflection about l.

Verify that the transformation f found in Problem 1 is an isometry.

Use the simplex method to determine whether the following LOP is optimal, unbounded, or infeasible.

Maximize z = x1 − x2

Subject to 2x1 − x2 = −5

x1 − 2x2 ≤ 3

−x1 + x2 ≤ −1

and x1 ≥ 0.

Solve the given integral equation for y(t):

y(t) + 10 ∫(0 to t)  cos(5(t−τ))y(τ)dτ = 6t

Given the sub-ring A = Z × Z ⊂ R ² ,Where, in R ² we have the sum operation and the complex product.

a) Prove that indeed A it is a sub-ring.

b) ¿It is A an entire domain?

c)Consider U = {(0, n) : n ∈ Z}, prove that U is an ideal of A.

d) Calculate A/U.

e) ¿It is U an ideal of R²?

I need all the paragraphs thanks

Given the differential equation (ax+b)²d²y/dx²+(ax+b)dy/dx+y=Q(x) show that the equations ax+b=e^t and t=ln(ax+b) reduces this equation to a linear equation with constant coefficients hence solve

(1+x)²d²y/dx²+(1+x)dy /dx+ y=(2x+3)(2x+4)

what are the thermal properties of composite materials??? with references, please.

Let C be the closed path that travels from (0, 0) to (1, 1) along y = x^2 , then from (1, 1) to (0, 2) along y = 2 − x^ 2 , and finally in a straight line from (0, 2) to (0, 0). Evaluate Z C e ^3−x √ 3 − x ) dx + (5x − y √ y^2 + 2) dy

give one of the major application of graph theory in real life

find the solution of the given initial value problem

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

2.    y''+4y=3sin2t, y(0) =2, y'(0) =-1

Question 4:
Oranges are grown, picked, and then processed and packaged at production centers in Sargodha,
Risalpur, and Sahiwal. These centers supply oranges to the company’s distributors each month in
Peshawar, Lahore, Multan, Faisalabbad, Karachi and Quetta.
Supplier Monthly Supply (Tons)
A. Sargodha 4,000
B. Risalpur 5,000
C. Sahiwal 3,500
12,500
The distributors, spread throughout six cities, have the following total monthly demand:
Distributor Monthly Demand (Tons)
1. Peshawar 1800
2. Lahore 2100
3. Multan 1700
4. Faisalabbad 1050
5. Karachi 2350
6. Quetta 1400
10,400
The company must pay the following shipping costs per ton:
to
from 1 2 3 4 5 6
A. $0.50 $0.35 $0.60 $0.45 $0.80 $0.75
B. 0.25 0.65 0.40 0.55 0.20 0.65
C. 0.40 0.70 0.55 0.50 0.35 0.50
(a) Determine the minimum cost shipping routes for the company using stepping stone
method.
(b) The Adams Fruit Company management has negotiated a new shipping contract with a
trucking firm between its Sargodha farm and its distributor in Karachi that reduces the
shipping cost per ton from $0.80 per ton to $0.55 per ton. How will this cost change
affect the optimal solution?
(c) Sometimes one or more of the routes in the transportation model are prohibited. That is,
units cannot be transported from a particular source to a particular destination. Because of
an agreement between distributors, shipments are prohibited from Sargodha to Quetta.
Shipments are also prohibited from Sahiwal to Lahore because of railroad construction,
what will be the effect on the optimal shipping routes? Solve this problem

Question 1. How many statements are true? (A) 0 (B) 1 (C) 2 (D) 3 (E) 4

Statement 1. Scheduled receipts are future receipts of past order releases

Statement 2. The MPS contains the GR of the end -item.

Statement 3. The POR is the inventory policy of the MRP

Statement 4. MRP minimizes cost.

Part 2. Questions 2,3,4.

Consider the end-item weekly MRPs for May 1 with Qd missing in each MRP. Match the correct MRP with the proper lot size discipline.