Show five (5) real-life examples on how to solve using Mathematical models. It should consist of topics under Algebra each (Rational, Exponential, Logarithmic, and Inverse Functions).  *Please show in clear, step-by-step solutions in scanned handwriting or computerized output.

Q: How many years will it take a $815 investment to be worth $1,392 if it continuously compound at 7%…

A:

Q: log (4x - 17) = 5

A:

Q: Evaluate the expression log10010 without using a calculator. If evaluation is not possible, state…

A: To evaluate log10010

Q: Express irrational solutions in exact form and as a decimal rounded to three decimal places. log2 (x…

A: Given: The equation  log2(x+1)-log4(x)=1

Q: Solve 3log5 13x + 12 - 2 log5 12x - 12 - log5 x

A: To simplify: 3log5(13x)+12-2log5(12x)-12-log5(x) Solution: 3log5(13x)+12-2log5(12x)-12-log5(x) On…

Q: Solve for x. log5 625 = x

A:

Q: Solve for 2x- 1 bl log4 (10-2)-0

A: (a) e2x-1 = 7 Taking log on both sides Ln (e2x-1) = Ln 7 (2x - 1) Ln (e ) = Ln 7.        { Ln ab = b…

Q: Express irrational solutions in exact form and as a decimal rounded to three decimal places. log2 x…

A: log2x-log6x=3

Q: 4. One yeast colony of 200 cells is growing exponentially by 10% each hour. Another yeast colony of…

A: To solve the following problem

Q: Acell population grows exponentially beginning with one cell. Which takes longer: increasing from…

A: Note that increasing from one to two cells means the population should be doubled. On the other hand…

Q: Suppose that the bacteria in a colony grow unchecked according to the Law of Exponential Change. The…

A: Given:    Since we have given that Number of bacteria initially = 1   It triples in number every 30…

Q: Evaluate the expression log3 38 without using a calculator. If evaluation is not possible, state the…

A:

Q: Is it possible to solve it without a pocket calculator ??

A: Here to evaluate: t=∫03ds(2.78s+0.8s3)12 The integral can't be evaluated manually.

Q: population doubles in size every 29 years assuming exponential growth, find the a. annual growth…

A:

Q: Express irrational solutions in exact form and as a decimal rounded to three decimal places. log9 x…

A: Use the log property to simplify the left side of the equation log9 x+3 log3 x=14. Use property…

Q: popultaion of a southern city folow exponential law.  if the population doubled in size over 14…

A:

Q: In the 2000 U.S. Census, a small city had a population of 45,000. By 2010, the population had…

A:

Q: How many years will it take a $766 investment to be worth $1,147 if it continuously compound at 1%…

A: We know that when interest is compounded yearly then amount is given as: A=P1+rnnt where, P is…

Q: A cell population grows exponentially beginning with one cell. Which takes longer: increasing from…

A: Definition of the exponential functions helps to find the answer to the problem. A function is said…

Q: Solve 6 - log, (3x - 2) = 4 for X %3D

A:

Q: Evaluate the expression log3(-9) without using a calculator. If evaluation is not possible, state…

A: Let the given value be y - y = log3-9Here, the solution to this problem is not possible because a…

Q: .Express in index notation: a) loga 8 = c ii. Simplify: 3log3 - log 27

A: I.Express in index notation:  a) loga 8 = cAnswerlogam=n ⇒ m=anThereforeloga8 = c ⇒8=ac

Q: Solve 3 log 80 - ln 5log 5

A: 3log80-ln5log5 Now, simplifying the above expression using the property of logarithms.…

Q: Evaluate the expression log100 0.1 without using a calculator. If evaluation is not possible, state…

A:

Q: A computer viruS can grow exponentially just like a real virus in a person's body. Suppose the…

A:

Q: Solve 2logs(Vx)- log;(6x– 1)=0.

A:

Q: Is there a way to do part 1 without derivates? We did not take calculus yet. This is from grade 11…

A: The equation modeling the resale value of a car is given below.

Q: Use a graphing device to find all solutions of the equation, rounded to two decimal places..³- - x =…

A:

Q: ) Solve for x: log4 x = 4

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: How are the two equations 102 = 100 and log10 100 = 2 related?

A: Here I am attaching image so that you understand each and every step.

Q: Evaluate the expression log16 4 without using a calculator. If evaluation is not possible, state the…

A: Evaluate: log16 4

Q: Solve for using the definition of logarithm: (logx+29)- 2=0

A:

Q: Solve exactly. 1 log64( – 5x + 3) – log64( – 7x + 1) - - 3 0 = || ||

A:

Q: Solve for x log64 x = 2

A: Explanation of the answer is as follows

Q: The half-life of carbon-14 is 5600 years. If a piece of charcoal made from the wood of a tree shows…

A: The half-life formula is given by: y=a(b)th...(1) where y is the final amount, a is the initial…

Q: A doctor prescribes 100 milligrams of a therapeutic drug that has decayed to 40% of its original…

A: We use radioactivity decay law

Q: Evaluate the expression log100 10 without using a calculator. If evaluation is not possible, state…

A: Evaluate the expression log100 10 without using a calculator.

Q: Evaluate the expression log2 8 + log5 25 without using a calculator. If evaluation is not possible,…

A: Given expression: log28+log525

Q: The half-life of carbon-14 is 5600 years. If a piece of charcoal made from the wood of a tree shows…

A:

Q: Solve for x. -7+ log, (x+3)=-5 %3D 5 ?

A:

Q: An average of 20 cars per hour arrive at the drive-inwindow of a fast-food restaurant. If each car’s…

A:

Q: Solve for x. logx 8 = 3

A:

Q: Solve for x. log4 (– 2x+4)=2

A:

Q: Express log,(9AB) in terms of log ,4 and log, Bin simplest form.

A:

Q: Solve for x. log 3(2x-5)=3

A:

Q: .show that log3n x = log3 x.Hence solve the equation log31 x + log3 x + log3 x = 13 n

A: We solve the given problem.

Q: A biologist is monitoring the population of a rare species of Jackelope. The initial population size…

A:

Q: Suppose that a population is 3000 at the beginning of 1980, and that it grows at 8% a year. What is…

A: Given:  Population is 3000 at the beginning of 1980, and that it grows at 8% a year.  To Find:…

Q: Find a formula for the exponential function passing through the points (-3, 6250) and (2, 2) f(x) =…

A: