Questions on Algebra: Exponent and logarithm as functions of power answered by real tutors!

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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(53339)

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(53339)

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(53339)

Question 742195: One pipe can fill a tank in 20 minutes, while
another takes 30 minutes to fill the same tank. How long would it take the two pipes together to fill the tank?

Click here to see answer by MathTherapy(10579)

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(53339)

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(53339)

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(53339)

Question 1181507: Determine the absolute deviation and the coefficient of variation.
𝑦=[200.432 (±0.002)]^1/2 / log(20.42 × 10^15(±0.06))
Click here to see answer by CPhill(2138)

Question 1209412: Find all real numbers x such that (3x - 27)^3 + (27x - 3)^3 = (3x + 27x - 30)^3.
Click here to see answer by Edwin McCravy(20077)

Question 1198664: An optical instrument with limiting magnitude L of any optical telescope and lens
diameter D, in inches, is given by
𝐿 = 8.8 + 5.1 𝑙𝑜𝑔 𝐷
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(2138)

Question 1209241: Can you explain the quotient rule and the power rule and how to tell the difference between them in example. I’m confused how you know the difference and what they mean by the power rule.
Click here to see answer by ikleyn(53339)

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(132)

Question 1208791: Solve for x.

12^(sqrt{x^2}) - 24^(x - 2) = 144
Click here to see answer by ikleyn(53339)

Question 1208832: Investing $8,000 for 6 years.
Option #1
7% compounded monthly
Option #2
6.85% compounded continuously
Which is the better investment?
Click here to see answer by ikleyn(53339)

Question 1208790: Solve for x.

5^(x + 2) + 6^x = 30
Click here to see answer by ikleyn(53339)

Question 1208811: Solve for x.
5^(sin x) - 5x + 10 = 0
Click here to see answer by ikleyn(53339)

Question 1208812: Solve for x.

12^(sin x + cos x) + 24x^2 = 0
Click here to see answer by greenestamps(13248)

Question 1208755: Find the range of y = e^x.

Click here to see answer by greenestamps(13248)

Question 1208756: Find the range of y = log[sqrt{e}].

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Question 1208757: Find the range of y = [[ 2x ]].

Note: [[ 2x ]] is a step function.
Click here to see answer by greenestamps(13248)

Question 1208600: Bismuth-210 is an isotope that radioactively decays by about 13% each day, meaning 13% of the remaining Bismuth-210 transforms into another atom (polonium-210 in this case) each day. If you begin with 215 mg of Bismuth-210, how much remains after 7 days?
After 7 days, mg of Bismouth-210 remains.
Round your answer to the nearest hundredth as needed.

Click here to see answer by math_tutor2020(3827)

Question 1208301: Hi can you help please:
int (3 x^3) (sqrt(16-x^2)) dx
Just not sure if my trig substitutions are working
Click here to see answer by mccravyedwin(417)

Question 1208301: Hi can you help please:
int (3 x^3) (sqrt(16-x^2)) dx
Just not sure if my trig substitutions are working
Click here to see answer by math_tutor2020(3827)

Question 1208301: Hi can you help please:
int (3 x^3) (sqrt(16-x^2)) dx
Just not sure if my trig substitutions are working
Click here to see answer by Edwin McCravy(20077)

Question 1208258: Hi, can you help me with part b please:
A particle is oscillating in Simple Harmonic Motion and is 𝑥 metres away from the origin after 𝑡 seconds. The movement of the particle can be modelled with the equation 𝑥 = 2 cos(3𝑡 + 𝛼)
a) Prove that its acceleration is −9𝑥 𝑚𝑠^-2.
b) If initially, 𝑥 = 1𝑚 with velocity 3√3 𝑚𝑠^-1, find a suitable value for 𝛼.
Click here to see answer by ikleyn(53339)

Question 1208255: Hi, can you help with this question:
Use x=alphasintheta for sqrt(alpha^2-x^2), x= alphatantheta for sqrt(alpha^2+x^2) and x= alphasectheta for sqrt(x^2-alpha^2), to find int (x/(sqrt(1-x^2)^3) dx
Click here to see answer by math_tutor2020(3827)

Question 1208235: log[5](x-2)=3 logarithm to exponential form
Click here to see answer by math_tutor2020(3827)

Question 1208235: log[5](x-2)=3 logarithm to exponential form
Click here to see answer by mananth(16949)

Question 1207550: Please help me solve the equation f(𝓍) = -log⅓ 3√𝓍 :
→ f(𝓍) = -log⅓ 3√𝓍
→ f(𝓍) = - ⅓ log⅓ 𝓍
→ f(𝓍) = ⅓ log3 𝓍

Click here to see answer by Edwin McCravy(20077)

Question 1207490: $5^{(}logx-1)/125=(1/5)^{(}logx)^{2}-logx$
Click here to see answer by Edwin McCravy(20077)

Question 1207490: $5^{(}logx-1)/125=(1/5)^{(}logx)^{2}-logx$
Click here to see answer by ikleyn(53339)

Question 1207302: The lengths of the sides of an equilateral triangle are log4(a), log10(b), log25(a+b) where A and B are positive numbers. What is the value of a/b?
Click here to see answer by ikleyn(53339)

Question 1207158: Log4x+log4(x-3)=1 find the solution
Click here to see answer by ikleyn(53339)

Question 1207158: Log4x+log4(x-3)=1 find the solution
Click here to see answer by Edwin McCravy(20077)

Question 1206983: how long would it take for 1000 deposited in an account payinv 6% interest compounded countinously to earn 200 interest
Click here to see answer by ikleyn(53339)

Question 1206952: a^3 - b^2 = 11
a^2 + b = 13
Click here to see answer by MathLover1(20854)

Question 1206832: The population of a colony of rabbits grows exponentially. The colony begins with 5 rabbits; 5 years later there are 320 rabbits.
(a) estimate how long it takes for the population of rabbits to reach 1000 rabbits.
Click here to see answer by Edwin McCravy(20077)

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