Mohammed Yaaseen Gomdah WeBWorK assignment number Assignment 4 W14 is due : 02/10/2016 at 03:00am EST. The (* replace with url for the course home page *) for the course contains the syllabus, grading policy and other information. MATH 203 Winter 2016 F This le is /conf/snippets/setHeader.pg you can use it as a model for creating les which introduce each problem set. The primary purpose of WeBWorK is to let you know that you are getting the correct answer or to alert you if you are making some kind of mistake. Usually you can attempt a problem as many times as you want before the due date. However, if you are having trouble guring out your error, you should consult the book, or ask a fellow student, one of the TA's or your professor for help. Don't spend a lot of time guessing - it's not very efcient or effective. Give 4 or 5 signicant digits for (oating point) numerical answers. For most problems when entering numerical answers, you can if you wish enter elementary expressions such as 2 ^ 3 instead of 8, sin(3 pi/2)instead of -1, e ^ (ln(2)) instead of 2, (2 + tan(3)) (4 sin(5)) ^ 6 7/8 instead of 27620.3413, etc. Here's the list of the functions which WeBWorK understands. You can use the Feedback button on each problem page to send e-mail to the professors. 5. (1 pt) Using the properties of logarithms, decide whether each equation is true or not. 1. (1 pt) Find the EXACT solution to the equation below (do not give a decimal approximation) . ? 1. ln (A) ln (B) = ln (A) + ln (B) log (A) ? 2. = log (A) log (B) log (B) ? 3. log (AB) = log (A) + log (B) p ? 4. log ( A) = 1 log (A) 2 p ? 5. ln (A) = ln (A(1/2) ) ? 6. p ln (A) = ln (A p ) log (x2 ) + log (x7 ) =3 log (19x) x= 2. (1 pt) The population of a colony of rabbits grows exponentially. The colony begins with 5 rabbits; 5 years later there are 390 rabbits. 6. (1 pt) Find the inverse function (if it exists) of h(x) = function is not invertible, enter NONE . (a) Express the population of the colony of rabbits, P , as a function of time, t , in years. P(t) = . If the h 1 (x) = (notice in this problem the independent variable in the inverse is x ) (b) Use the graph to estimate how long it takes for the population of rabbits to reach 1000 rabbits. It will take years. (round to nearest 0.01 year) 7. (1 pt) 3. (1 pt) Find the inverse function (if it exists) of f (x) = ln (7 If the function is not invertible, enter NONE . p If f (x) = , g(x) = 8x + 8 , and h(x) = x. Find a simplied formula for the function below: e8x 8x) . f 1 (x) = (notice in this problem the independent variable in the inverse is x ) f g(x) h(x) = 4. (1 pt) What is the domain of y = ln (x2 + 3x x 2x+3 8. (1 pt) 18) ? Find the inverse function of g(x) = is not invertible, enter NONE . click here for help using interval notation g 1 (x) = 1 p x+2 p 3 x . If the function (notice in this problem the independent variable in the inverse is x ) 10. (1 pt) Solve the following equation. If necessary, enter your answer as an expression involving natural logarithms or as a decimal approximation that is correct to at least four decimal places. 9. (1 pt) Find a formula for the inverse of the function. 22x+13 = 3x x f (x) = 1+ex . 1 e f 1 (x) = x= Generated by the WeBWorK system c WeBWorK Team, Department of Mathematics, University of Rochester 2 5