College Algebra Solve the following exponential equations, showing all work. 2. 4. e2-x 5. Given the following investment options, decide which one would benefit you the most after 6 years (make sure you show all work) a) You invest $5000 at 9.5% compounded monthly b) You invest $4500 at 8.25% compounded daily c) You invest $4750 at 9% compounded continuously 6. A certain strain of bacteria grows exponentially according to the model P(t)= P? is the initial population, k is the relative rate of growth, t is time in hours and P (t) is the population of bacteria for time t. Suppose we begin with 5 bacteria. After 1 hour, the number of bacteria has grown 75. How many bacteria will be present after 6 hours 7. The house down the street has termites in the porch. The exterminator estimated that there are about 525,000 termites eating at the porch. He said that the treatment he put on the wood would kill 32% of the termites every day. How many termites will be eating at the porch in 3 days For the following questions, write them in logarithmic form 8. 9. 10. 11. 13° = 1 For the following questions, write them in exponential form 12. log2 8=313. Log2 = 14. log = – 115. Log? s= t Expand each expression using the properties of logs 16. log3 (/y)17. Log2 / ) Write each expression as a single logarithm 18. 2 log(x) + 3 log(y) log(6)19. 5 log(a) 7 log(a) 2log(6) Use a calculator to find an approximation to the nearest thousandth for each of the following. 20. log.511421. Log 45,000 22. ln 12,00023. Ln 1.9 Solve each exponential or logarithmic equation. Show all work 24. log2 (x 1) – log2 (x + 2) = 225. = 7 26. + 3=1027. log4 (x + 2) = log8 8 28. ln(2x) ln(x 3) = 129. + 3 = 8 Determine whether the functions are inverses by using the composition of functions 30. f(x) = 6x + 42 g(x)=?x-7 31. f(x) = g(x) = (x-2) + 1 For each function, find out whether it is one-to-one. If the function is one-to-one, then find its inverse 32. f(x) = 3x + 233. f(x) = 3x 5 34. f(x) =
college_algebra_4.23.18.docx
Unformatted Attachment Preview
College Algebra
Solve the following exponential equations, showing all work.
1. 27?+1 = 9?
2. 22?-1 = 4
2. 8-?+14 = 16?
4. ? 3?+1 = e2-x
5. Given the following investment options, decide which one would benefit you the most after 6
years (make sure you show all work)
a) You invest $5000 at 9.5% compounded monthly
b) You invest $4500 at 8.25% compounded daily
c) You invest $4750 at 9% compounded continuously
6. A certain strain of bacteria grows exponentially according to the model
P(t)=????? ?h??? P? is the initial population, k is the relative rate of growth, t is time in hours
and P (t) is the population of bacteria for time t. Suppose we begin with 5 bacteria. After 1
hour, the number of bacteria has grown 75. How many bacteria will be present after 6 hours
7. The house down the street has termites in the porch. The exterminator estimated that there
are about 525,000 termites eating at the porch. He said that the treatment he put on the wood
would kill 32% of the termites every day. How many termites will be eating at the porch in 3
days
For the following questions, write them in logarithmic form
8. 63 = 216
10. 3-4
= 1/81
9.
1
1/4
(625)
11. 13° = 1
= 1/5
For the following questions, write them in exponential form
12. log2 8=3
14. log
4 3
=-1
3 4
3
13. Log2 v8 =2
15. Log? s= t
Expand each expression using the properties of logs
16. log3 (4? 2 /y)
4
17. Log2( v?? / ? 3 ? 2 )
Write each expression as a single logarithm
18. 2 log(x) + 3 log(y) log(6)
19. 5 log(a) 7 log(a) 2log(6)
Use a calculator to find an approximation to the nearest thousandth for each of the following.
20. log.5114
22. ln 12,000
21. Log 45,000
23. Ln 1.9
Solve each exponential or logarithmic equation. Show all work
24. log2 (x 1) – log2 (x + 2) = 2
26. 5?+4 + 3=10
28. ln(2x) ln(x 3) = 1
25. 42?-1 = 7
27. log4 (x + 2) = log8 8
29. 2? + 3 = 8
Determine whether the functions are inverses by using the composition of functions
30. f(x) = 6x + 42
g(x)=? x-7
31. f(x) = 3v? – 1 + 2
g(x) = (x-2)
3
+1
For each function, find out whether it is one-to-one. If the function is one-to-one, then find its
inverse
32. f(x) = 3x + 2
4
34. f(x) = ?-3
33. f(x) = 3x
3
5
…
Purchase answer to see full
attachment
Delivering a high-quality product at a reasonable price is not enough anymore.
That’s why we have developed 5 beneficial guarantees that will make your experience with our service enjoyable, easy, and safe.
You have to be 100% sure of the quality of your product to give a money-back guarantee. This describes us perfectly. Make sure that this guarantee is totally transparent.
Read moreEach paper is composed from scratch, according to your instructions. It is then checked by our plagiarism-detection software. There is no gap where plagiarism could squeeze in.
Read moreThanks to our free revisions, there is no way for you to be unsatisfied. We will work on your paper until you are completely happy with the result.
Read moreYour email is safe, as we store it according to international data protection rules. Your bank details are secure, as we use only reliable payment systems.
Read moreBy sending us your money, you buy the service we provide. Check out our terms and conditions if you prefer business talks to be laid out in official language.
Read more