Tutors Answer Your Questions about Exponential-and-logarithmic-functions (FREE)
Question 1023633: Using A=Pert formula, On March 11th 2011 a Fukushima reactor released 4.2 times the amount of cesium-137 as was leaked during 1986 Chernobyl disaster.
*half-life of cesium-137 is 30.2 years.
a.In what year will the cesium-137 level be half as much as immediately after the 2011 Fukushima disaster.
b.In what year will the cesium-137 level be a quarter as much immediately after 2011 Fukushima disaster?
c. How long after the disaster until the cesium-137 level is the same as immediately after the 1986 Chernobyl disaster.
Click here to see answer by jorel1380(3719)   |
Question 1024456: The value of China's exports of automobiles and parts (in billions of dollars) is approximately f(x)=1.8208e^.3387x, where x = 0 corresponds to 1998.
In what year did/will the exports reach $5.5 billion?
Give your answer as the year, with at least one decimal place
2. Students in a fifth-grade class were given an exam. During the next 2 years, the same students were retested several times. The average score was given by the model
f(t)=95−7log(t+1), 0≤t≤24 where t is the time in months. Round answers to at least 1 decimal point.
(a) What is the average score on the original exam?
(b) What was the average score after 6 months?
(c) What was the average score after 18 months?
Click here to see answer by jorel1380(3719) |
Question 1023887: Sam bought a home with a 30 year mortgage of $200,000 at an annual interest rate of 4.25%. Assuming Sam makes his monthly payment over the term of the loan, what will be the total amount of his payments? Also what will be his payment per month if he pays the same amount monthly?
Click here to see answer by jorel1380(3719) |
Question 1024454: Help Please
A bank features a savings account that has an annual percentage rate of r=4.7
% with interest compounded quarterly. Zach deposits $3,500 into the account.
The account balance can be modeled by the exponential formula S(t)=P(1+r/n)^nt
, where S is the future value, P is the present value, r is the annual percentage rate, n is the number of times each year that the interest is compounded, and t is the time in years.
(A) What values should be used for P, r, and n?
P=
r=
n=
B) How much money will Zach have in the account in 8 years?
Answer = $ . Round answer to the nearest penny.
2. The number of bacteria in a culture is given by the function
n(t)=955e0.25t where t is measured in hours.
(a) What is the relative rate of growth of this bacterium population?
Your answer is percent
(b) What is the initial population of the culture (at t=0)?
(c) How many bacteria will the culture contain at time t=5?
Click here to see answer by jorel1380(3719) |
Question 1077994: Suppose the quantity Q, in mg, of medicine in a patient’s bloodstream is decreasing by 25% each
40 minutes. Let us write Q = f(t), where t is in minutes since the injection of medicine. Suppose
the injection contains 300 mg of medicine.
(a) Construct a table of values for Q as a function of t over a few hours.
(b) Find a formula for f in the form A × B^t
, or an equivalent form.
(c) Let th be the time taken for the quantity of medicine in the bloodstream to halve. By a process
of guessing and checking, estimate the value of th (accurate to 3 significant figures).
(d) Determine the exact value of th.
(e) Show that the halving time is constant. That is, show that starting from an arbitrary time
t = a, the quantity of medicine is halved after an additional time th.
(f) Sketch a graph of the function over a 4 hour period since the injection.
(g) The patient can receive a new injection when the quantity of medicine is less than 2% of the
original dose. For simplicity, this time delay is measured in a whole number of hours. Determine
the wait time. For medicinal safety, should we round up or down to the nearest hour?
Click here to see answer by josgarithmetic(39620) |
Question 1077994: Suppose the quantity Q, in mg, of medicine in a patient’s bloodstream is decreasing by 25% each
40 minutes. Let us write Q = f(t), where t is in minutes since the injection of medicine. Suppose
the injection contains 300 mg of medicine.
(a) Construct a table of values for Q as a function of t over a few hours.
(b) Find a formula for f in the form A × B^t
, or an equivalent form.
(c) Let th be the time taken for the quantity of medicine in the bloodstream to halve. By a process
of guessing and checking, estimate the value of th (accurate to 3 significant figures).
(d) Determine the exact value of th.
(e) Show that the halving time is constant. That is, show that starting from an arbitrary time
t = a, the quantity of medicine is halved after an additional time th.
(f) Sketch a graph of the function over a 4 hour period since the injection.
(g) The patient can receive a new injection when the quantity of medicine is less than 2% of the
original dose. For simplicity, this time delay is measured in a whole number of hours. Determine
the wait time. For medicinal safety, should we round up or down to the nearest hour?
Click here to see answer by ikleyn(52802)  |
Question 1078034: problem: Doctors use radioactive iodine as a tracer in diagnosing certain thyroid gland disorders. This type of iodine decays in such a way that the mass remaining after t days is given by the function
m(t) = 2e^−0.087t
where m(t) is measured in grams.
(a) Find the mass at time t = 0. grams
(b) How much of the mass remains after 2 days? (Round your answer to three decimal places.)
Click here to see answer by josgarithmetic(39620) |
Question 1078701: If P dollars invested in an account that earns interest at 7% compounded annually the amount available after t years is A=P(1+1.07)^t. How many years will it take for $16000 in this account to grow to $22400?
Click here to see answer by Theo(13342)  |
Question 1080312: A computer that, when purchased 5 years ago cost $5,000 now has a value of $1,100. Find the value of the computer after 8 years by using the exponential model Vof(t) = V0ekt, in which Vof(t) is the value of the computer at any time t, V0 is the initial cost, and t is the time in years. Round your answer to the nearest hundredth.
Any help is greatly appreciated!
Click here to see answer by Theo(13342) |
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