Tutors Answer Your Questions about Exponential-and-logarithmic-functions (FREE)
Question 1055891: the logarithmic function f(x)= -100+87 in x models the number of visitors (in millions) to a certain country's museums, where x is the number of years since the initial recording of the number of visitors. use this function to estimate the number of visitors in year 60. Round to the nearest tenth of a year.
Click here to see answer by Alan3354(69443)   |
Question 1056046: (3 pts) Suppose y, the number of cases of a disease, is reduced by 12% per year.
(a) If there are initially 10,000 cases, express y as a function of t, the number of years elapsed.
y = (do not enter any commas in your formula)
(b) How many cases will there be 7 years from now?
cases.
(c) How long does it take to reduce the number of cases to 1000?
years
Click here to see answer by ewatrrr(24785)  |
Question 1056333: Please help me solve this question: The concentration (in milligrams per milliliter) of a certain drug in a patient's bloodstream
t hr after it has been administered is given by
C(t)=2te^-t/3 ,g/mL
Find the average concentration of the drug in the patient's bloodstream over the first 12 hr after
administration
Click here to see answer by Alan3354(69443) |
Question 1056771: Please help me to solve this problem.
Assume that the number of bacteria follows an exponential growth model: P(t)=P0ekt
. The count in the bacteria culture was 900 after 20 minutes and 1600 after 30 minutes.
(a) What was the initial size of the culture?
(b) Find the population after 80 minutes.
(c) How many minutes after the start of the experiment will the population reach 10000?
Click here to see answer by stanbon(75887) |
Question 1057455: The water in Midwestern lake contains sediment, and the presence of the sediment reduces the transmission of light through the water. Experiments indicate that the intensity of light is reduced by 10% by passage through 20 cm of water. Suppose that the lake is uniform with respect to the amount of sediment contained by the water. A measuring instrument can detect light at the intensity of 0.17% of full sunlight. This measuring instrument is lowered into the lake. At what depth will it first cease to record the presence of light? Give your answer to the nearest 10 cm.
Click here to see answer by josgarithmetic(39620) |
Question 1057693: Suppose a bank offers you a 4% interest rate on a 15-year mortgage to be paid back with monthly payments. The most you can afford to pay in monthly payments is $800. What is the maximum mortgage you can afford to take out for your home?
Click here to see answer by Boreal(15235)  |
Question 1057985: Hello,
I was asked (for homework) to solve the following without a calculator.
and
sin(1.5 degrees)
for the first one should I just do
by long hand ? Or do you think they are looking for somthing else?
I have no clue what to do for the second one.
Thanks for any help.
Click here to see answer by josgarithmetic(39620) |
Question 1058299: I don't understand how to use the appropriate formulas for these logarithmic models.
a) The hydrogen ion concentration of spinach is about 3.2 x 10^ -6 . Calculate the pH of spinach.
b) The pH of ammonia is 9.8 . Calculate its hydrogen ion concentration
c) A jet airplane generates 100 watts per square meter at a distance of 100 feet. Find the decibel level for a jet airplane.
Click here to see answer by josgarithmetic(39620) |
Question 1058417: The distance that a free falling object falls is directly proportional to the square of the time it falls (before it hits the ground). If an object fell 6060 ft in 44 seconds, how far will it have fallen by the end of 99 seconds? (Leave the variation constant in fraction form or round to at least 2 decimal places. Round your final answer to the nearest foot.)
Click here to see answer by ankor@dixie-net.com(22740)  |
Question 1058455: a.) The elevation of mt. Everest is 29028 feet, what is the atmospheric pressure at the top?
(hint: 1mile= 5280 feet)
b.) The atmospheric pressure at the top of the Mount McKinley is 13.51 inches of mercury. Estimate the elevation of Mount McKinley
Click here to see answer by Alan3354(69443) |
Question 1058775: I am looking for how I get the answer for:
ln(5x) = 3 + ln(x-1)
I move the natural logs to one side to make ln(5x) - ln(x-1) = 3, then use the properties of logarithms to get ln(5x/(x-1)) = 3.
I then make both sides a power of e to cancel out the ln and end up with 5x/(x-1) = e^3
I then multiply both sides by (x-1) to remove the fraction and get 5x = (e^3)x - e^3
Here is where I am stuck. I am unsure how to isolate the x. I know what the answer is supposed to be as this is a practice problem, but I don't know how to get there from here! And maybe I made a mistake in the process. Any help is greatly appreciated! Thank you!
Click here to see answer by rothauserc(4718)  |
Question 1058775: I am looking for how I get the answer for:
ln(5x) = 3 + ln(x-1)
I move the natural logs to one side to make ln(5x) - ln(x-1) = 3, then use the properties of logarithms to get ln(5x/(x-1)) = 3.
I then make both sides a power of e to cancel out the ln and end up with 5x/(x-1) = e^3
I then multiply both sides by (x-1) to remove the fraction and get 5x = (e^3)x - e^3
Here is where I am stuck. I am unsure how to isolate the x. I know what the answer is supposed to be as this is a practice problem, but I don't know how to get there from here! And maybe I made a mistake in the process. Any help is greatly appreciated! Thank you!
Click here to see answer by solve_for_x(190) |
Question 1059891: The mass of a radioactive substance follows a continuous exponential decay model, with a decay rate parameter of
2.3% per day. Find the half-life of this substance (that is, the time it takes for one-half the original amount in a given sample of this substance to decay).
Note: This is a continuous exponential decay model.
Do not round any intermediate computations, and round your answer to the nearest hundredth.
Click here to see answer by ankor@dixie-net.com(22740) |
Question 1060544: A research student is working with a culture of bacteria that doubles in size every twenty minutes. The initial population count was 1350 bacteria. Rounding k to six decimal places, write an exponential equation representing this situation. To the nearest whole number, what is the population size after 3 hours?
Click here to see answer by josgarithmetic(39620) |
Question 1060994: I'm not sure how to set up this problem.
a) Evaluate the expression in part (a) without using a calculator.
a) Use your result from part (a) to write the expression in part (b) as a single logarithm whose coefficient is 1.
91.) a) (log25)5
-For this I got 1/2
which is correct.
b.) (log25)x + (log25)(x^2-1) - (log25)(x+1) - 1/2
Really not sure what to do here.
But the answer in the book is two equivalent logarithmic expressions (separated by an equal sign.)
Click here to see answer by Alan3354(69443) |
Question 1060994: I'm not sure how to set up this problem.
a) Evaluate the expression in part (a) without using a calculator.
a) Use your result from part (a) to write the expression in part (b) as a single logarithm whose coefficient is 1.
91.) a) (log25)5
-For this I got 1/2
which is correct.
b.) (log25)x + (log25)(x^2-1) - (log25)(x+1) - 1/2
Really not sure what to do here.
But the answer in the book is two equivalent logarithmic expressions (separated by an equal sign.)
Click here to see answer by Theo(13342)  |
Question 1060994: I'm not sure how to set up this problem.
a) Evaluate the expression in part (a) without using a calculator.
a) Use your result from part (a) to write the expression in part (b) as a single logarithm whose coefficient is 1.
91.) a) (log25)5
-For this I got 1/2
which is correct.
b.) (log25)x + (log25)(x^2-1) - (log25)(x+1) - 1/2
Really not sure what to do here.
But the answer in the book is two equivalent logarithmic expressions (separated by an equal sign.)
Click here to see answer by josmiceli(19441)  |
Question 1060994: I'm not sure how to set up this problem.
a) Evaluate the expression in part (a) without using a calculator.
a) Use your result from part (a) to write the expression in part (b) as a single logarithm whose coefficient is 1.
91.) a) (log25)5
-For this I got 1/2
which is correct.
b.) (log25)x + (log25)(x^2-1) - (log25)(x+1) - 1/2
Really not sure what to do here.
But the answer in the book is two equivalent logarithmic expressions (separated by an equal sign.)
Click here to see answer by rothauserc(4718) |
Question 1061220: Hello! Thanks so much for considering helping me with my math question.
Suppose the population of a town is 3,400 in 2000. The population decreases at a rate of 2% every 20 years. What will be the projected population in 2040? Round your answer to the nearest whole number.
Click here to see answer by Cromlix(4381)  |
Question 1061222: I have been trying to figure out this answer for a while and need some help. If you could provide the steps that you went through to get the answer, that would be so helpful. Thank you so much!
You invest $3,000 in an account with an interest rate of 5.5% compounded continuously. How much money would be in the account after 5 years? Round your answer to the nearest whole number.
Click here to see answer by rothauserc(4718) |
Question 1061221: Hi! Thank you so much for your help. I would like to know how you get this answer, so if you could provide the steps you got to get the answer in addition to the answer, that would be most helpful. Thank you so much!
You invest an initial $4,500 in an account that has an annual interest rate of 4.5%, compounded daily. How much money will you have in the account after 10 years? Round your answer to the nearest whole number.
Click here to see answer by jorel555(1290) |
Question 1061473: As elevation above sea level increases, air pressure decays exponentially. The pressure at sea level is 1015 millibars while at 1800 feet it is 507.5 millibars. And the problem wants me to
A) Write the pressure as a function of elevation
B) Find the air pressure at 10000 feet elevation
Thanks a ton!
Click here to see answer by rothauserc(4718) |
Question 1061517: If you could show your steps as to how you get this answer, that'd be so great! Thank you.
You invest $1,300 in an account that has an annual interest rate of 5%, compounded annually. How much money will be in the account after 10 years? Round your answer to the nearest whole number.
Click here to see answer by addingup(3677)  |
Question 1061517: If you could show your steps as to how you get this answer, that'd be so great! Thank you.
You invest $1,300 in an account that has an annual interest rate of 5%, compounded annually. How much money will be in the account after 10 years? Round your answer to the nearest whole number.
Click here to see answer by LynnMomo(10)  |
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