Tutors Answer Your Questions about Exponential-and-logarithmic-functions (FREE)
Question 1149061: Abby opened a retirement account with 9% APR and initial deposit of $8,000 compounded monthly.
(a) Find the exponential function that models the value of Abby's retirement account after t years.
(b) How long will it take to double the initial value? Estimate your answer to the nearest year.
(c) How long will it take to triple the initial value? Estimate your answer to the nearest year.
(d) How long will it take for the value of the account to reach 7 times the value of the account after 2 years?
Click here to see answer by MathTherapy(10801)   |
Question 1104549: Please help me solve this word problem: in 1997, there were a total of 1,316,999 bankruptcies filed under the Bankruptcy Reform Act. The model for the number of bankruptcies filed is B(t)=0.798*1.164^t, where t is the number of years since 1994 and B is the number of bankruptcies filed in terms of millions (administrative office in US courts, statistical tables for the federal judiciary). In what year is it predicted that 12 million bankruptcies will be filed?
Click here to see answer by ikleyn(53742)  |
Question 1104549: Please help me solve this word problem: in 1997, there were a total of 1,316,999 bankruptcies filed under the Bankruptcy Reform Act. The model for the number of bankruptcies filed is B(t)=0.798*1.164^t, where t is the number of years since 1994 and B is the number of bankruptcies filed in terms of millions (administrative office in US courts, statistical tables for the federal judiciary). In what year is it predicted that 12 million bankruptcies will be filed?
Click here to see answer by josgarithmetic(39790) |
Question 1104549: Please help me solve this word problem: in 1997, there were a total of 1,316,999 bankruptcies filed under the Bankruptcy Reform Act. The model for the number of bankruptcies filed is B(t)=0.798*1.164^t, where t is the number of years since 1994 and B is the number of bankruptcies filed in terms of millions (administrative office in US courts, statistical tables for the federal judiciary). In what year is it predicted that 12 million bankruptcies will be filed?
Click here to see answer by MathTherapy(10801) |
Question 280462: This one looked easy but it's got me confused please help and thank you.
Use the laws of logarithms to express log base2 6 - log base 2 3 + 2 log base 2 sqrt8 as a single logarithm then evaluate. I got this far log base 2^6 - log base2^3 +2 log base 2 sqrt 8 =log base 2 6/3 sqrt8^2??? help
Click here to see answer by greenestamps(13325)  |
Question 280462: This one looked easy but it's got me confused please help and thank you.
Use the laws of logarithms to express log base2 6 - log base 2 3 + 2 log base 2 sqrt8 as a single logarithm then evaluate. I got this far log base 2^6 - log base2^3 +2 log base 2 sqrt 8 =log base 2 6/3 sqrt8^2??? help
Click here to see answer by MathTherapy(10801) |
Question 718152: Please help me solve for A and B in this exponential decay model y= ae^-bx. I have the following points: when x=0.6, y=1000 and when x=1.8, y=1.
I have done the following but I am not convienced it is the right path...
y=ae-bx therefor e-bx=y/a ... take log e of both sides ... loge e-bx = loge y/a
but logee=1 therefor -bx=loge y/a ... move the x over to get -b=x loge y/a
then enter values for x and y from example 1... -b= (0.6) loge(1000/a)
Is this the correct path to take for solving this?? Any advice would be greafull appreciated. Thank you.
Click here to see answer by greenestamps(13325) |
Question 718152: Please help me solve for A and B in this exponential decay model y= ae^-bx. I have the following points: when x=0.6, y=1000 and when x=1.8, y=1.
I have done the following but I am not convienced it is the right path...
y=ae-bx therefor e-bx=y/a ... take log e of both sides ... loge e-bx = loge y/a
but logee=1 therefor -bx=loge y/a ... move the x over to get -b=x loge y/a
then enter values for x and y from example 1... -b= (0.6) loge(1000/a)
Is this the correct path to take for solving this?? Any advice would be greafull appreciated. Thank you.
Click here to see answer by MathTherapy(10801) |
Question 31666: Oh this logarithm problems are killing me :)
Can you help! Write hte logarithm of a single expression:
log[b]6x+4(log[b]x-log[b]y)
(A) log[b] 6x^5/y^4
(B) log [b] 24x^2/y
(C) log [b] 10x/4y
(D) none of these.
Do we even consider the "B" in this expression?
Click here to see answer by MathTherapy(10801) |
Question 47675: Logarithms:
a) Using a calculator, find log 1000 where log means log to the base of 10.
Answer:
b) Most calculators have 2 different logs on them: log, which is base 10, and ln, which is base e. In computer science, digital computers are based on the binary numbering system which means that there are only 2 numbers available to the computer, 0 and 1. When a computer scientist needs a logarithm, he needs a log to base 2 which is not on any calculator. To find the log of a number to any base, we can use a conversion formula as shown here:
Using this formula,a=log a/log b, find log2 1000 . Round your answer to the hundredth's place.
Answer:
Show work in this space.
Click here to see answer by MathTherapy(10801) |
Question 253889: beryllium-11 decomposes into boron-11 with a half life of 13.8 seconds. How long will it take 240 g of beryllium-11 to decompose into 7.5g of beryllium-11?
based on the forumula provided in the text book C(t)=C(0)2e^-t/h
where C(0) = 240, C(t)=7.5 ,h=13.8
7.5/240=2e^-t/13.8
this was a s far as i got
Click here to see answer by ikleyn(53742) |
Question 253874: beryllium-11 decomposes into boron-11 with a half life of 13.8 seconds. How long will it take 240 g of beryllium-11 to decompose into 7.5g of beryllium-11?
based on the forumula provided in the text book C(t)=C(0)2e^-t/h
where C(0) = 240, C(t)=7.5 ,h=13.8
7.5/240=2e^-t/13.8
this was a s far as i got
Click here to see answer by ikleyn(53742) |
Question 730115: Berlyium-11 decomposes into boron-11 with a half life of 13.8 seconds. How long will it take 2400g of berlyium-11 to decompose into 75g of berlyium-11?
Thats the question, and I tried solving it but im stuck. This is what I have so far:
75=2400 x 2^-t/13.8
0.01325=27.6 (-t)
Click here to see answer by ikleyn(53742) |
Question 617971: Solve the problem.
The logistic growth function f(t) = 400/1+9.0e-0.22t describes the population of a species of butterflies after they are introduced to a non-threatening habitat. How many butterflies are expected in the habitat after 12 months?
Click here to see answer by ikleyn(53742) |
Question 475306: The annual Gross Domestic Product (GDP) of a country is the value of all of the goods and services produced in the country during a year. During the period 1985-1999, the Gross Domestic Product of the United States grew about 3.2% per year, measured in 1996 dollars. In 1985, the GDP was $577 billion.
In what year will the GDP reach $2 trillion? You just need to give the year, not part of a year.
Click here to see answer by ikleyn(53742) |
Question 481218: Compound Interest formula:
A= P(1+(r/n))^nt
I have to use this formula to answer this question:
Determine how much time is required for an investment to double in value if interest is earned at a rate of 6.25% and compounded annually?
Please give me a detailed answer, I have tried using the formula myself but I keep getting stuck and am not having much success.
Thank you in advance for all your help! I really do appreciate it.
Click here to see answer by ikleyn(53742) |
Question 1198664: An optical instrument with limiting magnitude L of any optical telescope and lens
diameter D, in inches, is given by
šæ = 8.8 + 5.1 ššš š·
a) Determine the limiting magnitude for a homemade I -inch reflecting telescope.
b) Determine the diameter of a lens that would have a limiting magnitude of R.
Click here to see answer by CPhill(2189)  |
Question 1209240: A biologist is researching a newly discovered species of bacteria. At time T equals zero hours, he put 100 bacteria into what he has determined to be a favorable growth medium. Six hours later, he measures 450 bacteria. Assuming exponential growth, what is the growth constant K for the bacteria? (Round K2 decimal places) By what hour to the nearest 10 will there be 1000 bacteria?
Click here to see answer by timofer(155) |
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