Tutors Answer Your Questions about Exponential-and-logarithmic-functions (FREE)
Question 959994: For some reason this question did not get posted the last time I asked, so I'm having to post it again.
In this problem I've been asked to prove that loga x = c * logb x, where c is a constant. In other words, direct proportionality. I'd started out by representing the left side of the above equation with p and the right with q, then went (left side)/p = 1 and (right side)/q = 1, therefore (left side)/p = (right side)/q. I then cross-multiplied and used the division property of equality to get... exactly what I already had, (left side)/p = (right side)/q. Just when I thought I had it cracked too! A later problem has provided a clue - if c were equal to loga b, that might be very helpful, but I can't figure out how to get there without making that a given.
I'm completely stumped here. Help!
Click here to see answer by josgarithmetic(39620)  |
Question 960976: i have a question about a problem that my parents gave me. the problem is  . here's what I've done.
x<0
3x=-4
x=
my dad says that I am missing a step in between the third and fourth step. I've been thinking about it for 10 minutes, but i can't figure out whats missing. it makes sense to me. please help?
Click here to see answer by josgarithmetic(39620) |
Question 960998: Here is the problem:
A certain item costs $4.75. Due to inflation, experts estimate the cost will increase by 2% per year. Approximately how many years until the item costs $7.20?
Do I use the growth formula to solve???
Q(t) = C * (1+r/t)^t
Solve for t to get the answer???
Click here to see answer by harpazo(655)  |
Question 960997: I need help with these questions:
A certain amount of Californium-251 is slowly decaying. After 101 years 92.5 grams of an initial 100 grams are remaining.
a. Create a function, Q(t), that will calculate how much Californium-251 is remaining after t years.
b. What is the approximate half-life of Californium-251?
This is what I did for part a:
92.5 - 100(x)^101
.925 = x^101
I got stuck after that. I don't know how to solve for 'x'
This is what I did for part b:
Q(t) = 100(1/2)t/101
t = 101 - is this correct????
Click here to see answer by ankor@dixie-net.com(22740)  |
Question 962124: Graph f(x) = (-logbase5*(2x)) -1
Could someone please walk me though each step? I understand that the graph is reflected over the x-axis, and that the whole thing is translated down one unit. However, I don't know how to figure out each point that I need.
Thank you for your help!
Click here to see answer by josmiceli(19441)  |
Question 962262: 22. Vapor Pressure Problem: The vapor pressure of water is the pressure that water vapor (steam) would exert if it, alone, occupied the space above the water in a closed container. About 200 years ago French scientists Clausius and Clapeyron found that the vapor pressure varies exponentially with the reciprocal of the absolute temperature of the water. That is, if P is the vapor pressure and T is the absolute temperature, then P = a x 10^((k x (1/T))
a. Find the particular equation expressing vapor pressure in terms of absolute temperature if water at 0 degrees Celsius has a vapor pressure of 4.6 millimeters of mercury (mm), and at 100 degrees Celsius, has 760 mm. (The absolute temperature is 273 plus the Celsius temperature.) You must be very clever to figure a way to evaluate the two constants!
b. Use your equation to predict the vapor pressure of water on a hot summer day, 40 degrees Celsius.
c. Water boils when it's vapor pressure reaches the pressure if its surrounding atmosphere. At what Celsius temperature would water boil
i. atop Mt. Everest, where the air is 220 nm?
ii. in the reactor of a nuclear power plant, where the pressure is kept at 100,000 mm?
iii. in the deepest part of the ocean, where the pressure is 800,000 mm?
Click here to see answer by stanbon(75887) |
Question 963554: According to Newton's Law of Cooling, if a body with temperature T 1 is placed in surroundings with temperature T 0, different from that of T 1, the body will either cool or warm to temperature T(t) after t minutes, where:
T(t) = T 0 + (T 1 - T 0)e^(kt)
and k is a constant.
A cup of coffee with temperature 140°F is placed in a freezer with temperature 0°F. The constant k ≈ -0.0815. Use Newton's Law of Cooling to find the coffee's temperature, to the nearest degree Fahrenheit, after 15 minutes.
Click here to see answer by Fombitz(32388)  |
Question 964524: Hello I really need help with this word problem
a radioactive isotope decays exponentially. the time it takes for half of the amount to decay is called the isotopes half-life. A certain isotope has a half-life of 12 hours. if after 72 hours there are 0.325 mg left, what was the isotopes initial mass?
Click here to see answer by josgarithmetic(39620) |
Question 966057: Exponential Regression
The table below shows the value, V, of an investment (in dollars) after n years.
n 0 3 7 12 14 19
V(n) 2300 2391.96 2641.98 3004.46 3034.8 3183.13
Use your calculator to determine the exponential regression equation that models the set of data above. Round the "a" value to two decimals, and round the "b" value to three decimals. Use the indicated variables and proper function notation.
V(n) =2308.43(1.019)^n I was able to solve this part of the problem
Based on the your regression model, what is the percent increase per year?
1.9% I was able to solve this part of the problem
Find V(20). Round your answer to two decimal places.
V(20) = I came up with $3,243.61
How long will it take for the value of this investment to reach $11,500? Round your answer to two decimal places.
V(n) = 11500 when n =
I wasn't able to solve this part of the problem
How long will it take for the value of the investment to double? Round your answer to two decimal places.
V(n) has doubled when n =
I wasn't able to solve this part of the problem
Click here to see answer by jim_thompson5910(35256) |
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Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445, 5446..5490, 5491..5535, 5536..5580, 5581..5625, 5626..5670, 5671..5715, 5716..5760, 5761..5805, 5806..5850, 5851..5895, 5896..5940, 5941..5985, 5986..6030, 6031..6075, 6076..6120, 6121..6165, 6166..6210, 6211..6255, 6256..6300, 6301..6345, 6346..6390, 6391..6435, 6436..6480, 6481..6525, 6526..6570, 6571..6615, 6616..6660, 6661..6705, 6706..6750, 6751..6795, 6796..6840, 6841..6885, 6886..6930, 6931..6975, 6976..7020, 7021..7065, 7066..7110, 7111..7155, 7156..7200, 7201..7245, 7246..7290, 7291..7335, 7336..7380, 7381..7425, 7426..7470, 7471..7515, 7516..7560, 7561..7605, 7606..7650, 7651..7695, 7696..7740, 7741..7785, 7786..7830, 7831..7875, 7876..7920, 7921..7965, 7966..8010, 8011..8055, 8056..8100, 8101..8145, 8146..8190, 8191..8235, 8236..8280, 8281..8325, 8326..8370, 8371..8415, 8416..8460, 8461..8505, 8506..8550, 8551..8595, 8596..8640, 8641..8685, 8686..8730, 8731..8775, 8776..8820, 8821..8865, 8866..8910
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