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

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Question 1041884: The purchasing power of A dollars after t years of r% inflation is given by the model P = Ae^-rt. Assume the inflation rate is currently 3.8%. How long will it take for the purchasing power of $1.00 to be worth $0.76? Round the answer to the nearest hundredth.
I already got the answer, but it would be great if someone could explain how to solve it.
Click here to see answer by Theo(13342)

Question 1042284: Solve 4.3^x+1 =27+9^x
Click here to see answer by ikleyn(52802)

Question 1042443: Which of the following would best represent a cosine function with an amplitude of 2, a period of pi over 3, and a midline at y = 1

Click here to see answer by robertb(5830)

Question 1042446: Where are the asymptotes of f(x) = tan 4x from x = 0 to x = pi over 2
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Question 1042445: How does changing the function from f(x) = 3 sin 2x to g(x) = 3 sin 2x + 5 affect the range of the function?
Click here to see answer by Edwin McCravy(20060)

Question 1042447:
What is the rate of change for f(x) = −2 cos 4x − 3 on the interval from x = 0 to x = pi over 4 ?
Click here to see answer by Alan3354(69443)

Question 1042475: 6^3n = 43^5n-4
Solve for n. Round to four decimal places.
A.1.1202
B.-1.9005
C.-0.2800
D.2.1418
Click here to see answer by stanbon(75887)

Question 1042475: 6^3n = 43^5n-4
Solve for n. Round to four decimal places.
A.1.1202
B.-1.9005
C.-0.2800
D.2.1418
Click here to see answer by MathTherapy(10552)

Question 1042538: Which of the following would best represent a cosine function with an amplitude of 2, a period of pi over 3, and a midline at y = 1?
I need to show work
Click here to see answer by josmiceli(19441)

Question 1042541: In Crescent Moon Bay in July, high tide is at 3:00 pm. The water level is 6 feet at high tide and 2 feet at low tide. Assuming the next high tide is exactly 12 hours later and the height of the water can be modeled by a cosine curve, find an equation for Crescent Moon Bay's water level in July as a function of time (t).
need to show work
Click here to see answer by josmiceli(19441)

Question 1042536: If sin θ = 2 over 7 and tan θ > 0, what is the value of cos θ?
I have to show work
Click here to see answer by Fombitz(32388)

Question 1042540: What is the rate of change between the interval x = π and x = three pi over two ?
I know the answer is -16/pi
need to show work
Click here to see answer by Fombitz(32388)

Question 1042537: If sin θ = 2 over 7 and tan θ > 0, what is the value of cos θ?
I need to show work
Click here to see answer by ikleyn(52802)

Question 1042649: What is the solution of log4x − 616 = 4
Click here to see answer by rothauserc(4718)

Question 1042683: How do I find the equation for an exponential in the form y=Ae^kx that passes through the points (0,1) and (7,8)?
Click here to see answer by ikleyn(52802)

Question 1042448: In Crescent Moon Bay in July, high tide is at 3:00 pm. The water level is 6 feet at high tide and 2 feet at low tide.
Assuming the next high tide is exactly 12 hours later and the height of the water can be modeled by a cosine curve,
find an equation for Crescent Moon Bay's water level in July as a function of time (t).
Click here to see answer by ikleyn(52802)

Question 1042989: how do I write an exponential function of a graph passing through these two points 1,6 and 1,3 ?
Click here to see answer by ankor@dixie-net.com(22740)

Question 1043030: Having a really hard time with this questions. It asks to solve 100(1.02)^x/4=200. Could you please show the steps so I can understand it?
Click here to see answer by ankor@dixie-net.com(22740)

Question 1043172: Simplify 27^0.5�64^1/3�81^0.25
THANK YOU
Click here to see answer by Fombitz(32388)

Question 1043476: what is the answer of log=246.9 and anti log =2.4015
Click here to see answer by Alan3354(69443)

Question 1043638: A house has been infested with termites, and the infestation is represented by the growth function, f(t)=55001+30e−0.5t, which describes the number of termites present t days after the initial outbreak.
Find the following:
A) Find the number of termites present at the initial outbreak. (Round your answer to the nearest whole number.)
Answer = approximately termites
B) Find the termite population after 8 days. (Round your answer to the nearest whole number.)
Answer = approximately termites

Click here to see answer by advanced_Learner(501)

Question 1044261: Simplify e^(1+lnx)
Click here to see answer by Fombitz(32388)

Question 1044381: if f(x)=|x-2| then find f(-3)
Click here to see answer by ikleyn(52802)

Question 1044408: What is log6 x=2.1?
Click here to see answer by Alan3354(69443)

Question 1044458: If 40 mg of a radioactive substance decays to 5 mg in 12 minutes, find the half life of the substance in minutes.
Click here to see answer by josgarithmetic(39620)

Question 1044459: e^(3x)=4x^2
Click here to see answer by ikleyn(52802)

Question 1044778: Solve the equation 1/(7^x)= 3*49^(5-x), giving your answer in the form a+ log(base 7)b where a,b are integers.
Click here to see answer by josgarithmetic(39620)

Question 1044890: F(x)=[logx] where [] is greatest integer function ...set of zeros of f(x)???
Click here to see answer by Edwin McCravy(20060)

Question 1044917: solve 2^0/2^-2
Click here to see answer by ikleyn(52802)

Question 1045014: Kindly help me in this problem
If
then

Or

Or

Or
None of these
I tried it in the following manner
Let us assume that

So

And
But i can't go further please help by showing complete calculations
Click here to see answer by josgarithmetic(39620)

Question 1045259: Help need with this question. Detailed workings would be very much appreciated, thanks.
Joe decided to undergo an advanced typing course for 20 weeks and he progresses according to the function
Q(t) = 130(1-e^(-0.05t) ) +65
where Q(t) is the number of words per minute Joe can type after t weeks in the course.
1) What is the initial typing speed of Joe in this course?
2) Find the typing speed of Joe halfway through the course.
3) In which week will Joe�s typing speed reach 100 words per minute?

Click here to see answer by advanced_Learner(501)

Question 1045550: Solve log2 8^3
Click here to see answer by advanced_Learner(501)

Question 1045550: Solve log2 8^3
Click here to see answer by MathTherapy(10552)

Question 1045983: At t=0 , there were initially 20 bacteria. Suppose that the bacteria doubles every 100 hours. Give an exponential model for the bacteria as a function t.
Click here to see answer by josmiceli(19441)

Question 1046317: Martha can rake the leaves in her yard in 2 hours. Her younger brother can do the job in 6 hours. How long will it take them to do the job if they work together? please show work and thank you
Click here to see answer by josgarithmetic(39620)

Question 1046612: Condense the following equations:
a.) x^4 X x^15
b.) x^a X x^b X x^c
c.) x^3 X y^3 X z^3
Click here to see answer by Alan3354(69443)

Question 1046920: What are composite functions? How do you write them?
Click here to see answer by josgarithmetic(39620)

Question 1046940: solve this equation and inequality a) (X-7)(X+3)= -9
b) ≤-2x ≥ 11
Click here to see answer by josgarithmetic(39620)

Question 1047799: evaluate log12 3 + log12 48
Click here to see answer by Alan3354(69443)

Question 1047799: evaluate log12 3 + log12 48
Click here to see answer by ikleyn(52802)

Question 1047798: log12 3 + log12 48
Click here to see answer by Alan3354(69443)

Question 1048183: Solve for x:
a) (3/5)^x+1 = 25/9
b) (49/81)^x+1 > 9/7
Click here to see answer by Alan3354(69443)

Question 1048435: Compute derivative of the following function by two different methods.
f(x) = (x^3 + 1)(x^2 + 2)

Click here to see answer by ewatrrr(24785)

Question 1048581: Please help me solve this question
4. The number of certain species of fish introduced into a lake is 1500.
Five years later the population of the species reaches 2150.
(a) Find the relative growth rate of the population.
(b) How long would it take for the population to triple?
(c) Find the function that models the population of the species
t years from now.

Click here to see answer by josgarithmetic(39620)

Question 1048578: Please help me solve this question
2. The rate of decay of a radioactive substance is 0.1% per year.
(a) Find the half-life of the substance.
(b) How long would it take until only 1/2 of the amount remains?
(c) How long would it take until 2/3 of the original amount decays?
(d) How much of the 10 mg sample of the substance will remain after
5,000 years?

Click here to see answer by josgarithmetic(39620)

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