Solve the following logarithmic equations, Engineering Mathematics

Assignment Help:

1. Joe and Sam each invested $20,000 in the stock market. Joe's investment increased in value by 5% per year for 10 years. Sam's investment decreased in value by 5% for 5 years and then increased by 12.5% for the next 5 years. AT the end of 10 years, what was the value of each person's investment?

2. Investigate the following functions for both horizontal and vertical asymptotes, x and y-intercepts, and state the domain and range of each and where the function is increasing and decreasing.     (A)  f(x) = (2x3 - 3x - 5)/(x3 - 8).                                                            (B) g(x) = (x - 3)/(x2 - 5x  + 6)

3. A manufacturing company wants to package its product in a rectangular box with a square base and a volume of 32 cubic inches. The cost of the material used for the top is $.05 square inch; the cost of the material used for the bottom is $.15 per square inch, and the cost of the material used for four sides is $.10 per square inch. What are the dimensions of the box with the minimum cost?

4. In planning a restaurant, it is estimated that a revenue of $6 per seat will be realized if the number of seats is at most 50. On the other hand, the revenue on each seat will decrease by $.10 for each seat exceeding 50 seats. Find the revenue function where x = the number of seats exceeding 50 seats. What is the maximum revenue and what number of seats generates that maximum revenue.

5. You invest $1,000 at an annual interest rate of 5% compounded continuously. How much is your balance after 8.5 years?  How long will it take you to accrue a balance of $4,000? What interest rate is required to yield a balance of $7,000 after 7 years?

6. A sum of $2,500 is deposited in a bank account that pays 5.25% interest compounded weekly. How long will it take for the deposit to double?  How long will it take you to accrue a balance of $7,500?  What interest rate is required to yield a balance of $7,000 after 7 years?

7. Solve the following logarithmic equations. A) log(x-1)  - log(x+1) = 1; B) ln(x) = -1.147; C) ln(x) =  (2/3)ln(8) + (1/2)ln(9) - ln(6); D) log5 (x) + log5 (x-4) = log5 (21);  E) log4 (3x) - log4 (x2-1) = log4 (2)

8. Solve the following exponential equations. A) 3(7x+1) =  3(4x-5); B) 8x  =  2(x-6); C)  3(x+2) = 5: D)  4(x) = 2(3x+4); E) e(x - 6) = 3.5.

9. Graph f(x) = 2x - 3 and approximate the zero of f to the nearest tenth. Also find the y-intercept and any horizontal and vertical asymptotes.

10.  In a research experiment, a population of fruit flies is increasing according to the law of exponential growth. After 2 days there are 100 flies, and after 4 days there are 300 flies. How many flies will there be after 5 days?


Related Discussions:- Solve the following logarithmic equations

A high school counselor, A high school counselor needs to specify whether t...

A high school counselor needs to specify whether the teenage pregnancy rate at her school is disimilar from the rate nationwide. She knows that the rate nationwide is 15 %. She ran

Expression to be programmed in matlab, can you help be please to program a ...

can you help be please to program a complex expression in matlab using monte carlo solution

Value of n, Arrianna spended $5,500 at 7.5% p.a. compounded quarterly for '...

Arrianna spended $5,500 at 7.5% p.a. compounded quarterly for 'n' years. At the end of 'n' years, Arrianna got back $12,000. What is the value of n? (Approximate your answer in yea

Two distinct case, A) Prove the following theorem by considering two distin...

A) Prove the following theorem by considering two distinct cases. For any integer n, n 2 + n is even. B)  If x = r 2  - s 2 and y = 2rs for any integers r and s, then x 2 +

MEAN VALUE THEORM, APPLICATIONS OF LAGRANGE''S MEAN VALUE THEORM?

APPLICATIONS OF LAGRANGE''S MEAN VALUE THEORM?

Dynamics, The acceleration of an oscillating particle is defined by the rel...

The acceleration of an oscillating particle is defined by the relation a = -kx Determine the value of k such that v = 15 in./s when x = 0 and x = 3 in. and v = 0, the speed of the

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd