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

Tutors Answer Your Questions about Exponential-and-logarithmic-functions (FREE)

Question 1148012: Solve the equation.
16^(8x) · (1/4)^(3x + 8)= 64 · (4x)^−6
Click here to see answer by ikleyn(52800)

Question 1148043: A drug is eliminated from the body through urine. Suppose that for an initial dose of 10 milligrams, the amount A(t) in the body t hours later is given by A(t) = 10(0.8)^t.
What percentage of the drug still in the body is eliminated each hour
Click here to see answer by ikleyn(52800)

Question 1148044: Suppose the price of a first-class stamp was 4¢ for the first time in 1958 and 44¢ in 2009. Find a simple exponential function of the form
y = ab^t that models the cost of a first-class stamp for 1958 - 2009. (Let
t = 0 correspond to 1958. Assume y is in dollars. Round your value for b to four decimal places.)
y=???
Also how would i predict tha value for 2020?
Click here to see answer by greenestamps(13200)

Question 1148042: The population N(t) (in millions) of a country t years after 1980 may be approximated by the formula N(t) = 213e^(0.0101t).
When will the population be twice what it was in 1980? (Round your answer to one decimal place.)
Click here to see answer by josgarithmetic(39620)

Question 1148255: How many 3 digit palindromes are divisible by 9?

Click here to see answer by Alan3354(69443)

Question 1148543: Find the exponential function
f(x)=Ca^x
whose graph goes through the points
(0,2)and (3,16).
Click here to see answer by psbhowmick(878)

Question 1148543: Find the exponential function
f(x)=Ca^x
whose graph goes through the points
(0,2)and (3,16).
Click here to see answer by greenestamps(13200)

Question 1148670: Graph the function f(x)= 6^(x+5)
Click here to see answer by Alan3354(69443)

Question 1148774: y = 80.7 - 11 ln x, 100 ≤ x ≤ 1500 which approximates the minimum required ventilation rate in terms of the air space per child in a public school classroom. In the model, x is the air space per child in cubic feet and y is the ventilation rate in cubic feet per minute.
a)Estimate the required rate of ventilation in a room with 300 cubic feet of air space per child ... (answer is 17.96 cubic feet/min/child)
b) A classroom of 30 students has an air conditioner system that moves 450 cubic feet of air per minute. Find rate of ventilation ... (answer is 15 cubic feet/min/student)
c) Use part a) to estimate the minimum required air space per child for the classroom in part b) ...... That's what I need help with
Click here to see answer by ikleyn(52800)

Question 1148883: 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 Alyssa’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 ikleyn(52800)

Question 1148923: The population of a colony of rabbits grows exponentially. The colony begins with 15 rabbits; 5 years later there are 380 rabbits
Click here to see answer by josgarithmetic(39620)

Question 1149062: (a) Solve the equation −(1/2)^(x+1)+4=2
(b) Graph the equation -(1/2)^(x+1)+4=2
Click here to see answer by Alan3354(69443)

Question 1149069: Find the time required for an investment of 5000 dollars to grow to 8300 dollars at an interest rate of 7.5 percent per year, compounded quarterly.
Click here to see answer by Theo(13342)

Question 1149070: Find the solution of the exponential equation
1000(1.05)^(2t)=5,000
in terms of logarithms, or correct to four decimal places.
Find T?
Click here to see answer by greenestamps(13200)

Question 1149231: The amount of radioactive substance present, in grams, at time t, in years, is given by the formula
y=20(3)^-0.6t.
Find the number of grams present in 4 years.
Click here to see answer by greenestamps(13200)

Question 1149320: find the value of k. P(t)=5400e^kt
Click here to see answer by josgarithmetic(39620)

Question 1149320: find the value of k. P(t)=5400e^kt
Click here to see answer by ikleyn(52800)

Question 1149409: Trouver toutes les valeurs réelles de x pour lesquelles l'inégalité suivante est satisfaite:
Log4(x+3)+log16(x)<1
où log4 représente le logarithme en base 4 et log 16 celui en base 16
Click here to see answer by rothauserc(4718)

Question 1149410: Résoudre dans R : Arccos (2x) - Arccos(x) = π/3
Click here to see answer by ikleyn(52800)

Question 1149568: From 1992 to 1994, the population of California grew by 14.9 percent to 981,169. The area gets its water from the Colorado river and underground sources and has enough to support 1.6 million people.
a) What was the population in California in 1992?
b) How many years will it be before the population of California reaches the maximum number of people for which it can supply water. Explain your answer.
Click here to see answer by ikleyn(52800)

Question 1149578: The half-life of strontium -90 is 28 years. How much of a 10-g sample will remain after:
a) 1 year?
b) 10 years?
Click here to see answer by ikleyn(52800)

Question 1149578: The half-life of strontium -90 is 28 years. How much of a 10-g sample will remain after:
a) 1 year?
b) 10 years?
Click here to see answer by Alan3354(69443)

Question 1149576: Suppose that a character from a 1960 movie, is normally 180cm tall, but each succeeding minute he shrinks to 99% of his size of the previous minute.
a) How tall is he after 1 hour? After 2 hours?
b) How long will it take him to become 1 cm tall?
Click here to see answer by Alan3354(69443)

Question 1149406: Let f be a real-valued function such that f(x-f(y)) = f(x) - xf(y) for any real numbers x and y. If f(0)=3, determine f(2016) - f(2013).
Click here to see answer by Edwin McCravy(20059)

Question 1149577: In x minutes, there will be f(x) bacteria present in a certain culture, where f(x)=Ae raised to 0.03x. If 100,000 bacteria are present initially,
a) How many will be present in 1 minute?
b) After how many minutes will there be 200,000 present?
Click here to see answer by Alan3354(69443)

Question 1149572: The intensity of light under water decreases by 3.5% for every meter one descends. The function y=100(0.975) raised to x shows the relationship between the depth in meters (x) and the percent of surface light intensity that reaches the depth. Estimate the percent of light intensity that reaches the depths of 15 meters and 85 meters.
Click here to see answer by greenestamps(13200)

Question 1149569: Suppose the equation b=5(0.8) raised to x shows the relationship between the number of bounces (x) and the height of the bounce (b) in feet, What is the height of the fifth bounce? What is the height of the 100th bounce?
Click here to see answer by greenestamps(13200)

Question 1149567: Since 1950, the world population has risen from 2.5 billion at a rate of 1.8% per year. The equation that represents this exponential function is y=2.5(1.018) raised to x, where x represents the time in years since 1950, and y represents the world population, in billions. Estimate the population in a) 1976, b)2001, and c)2026.
Click here to see answer by greenestamps(13200)

Question 1149566: Suppose that at the start of an experiment in a biochem class, 15 bacteria are present in a colony. Five hours later, the population is found to be 35.
a) Determine the constant c.
b) How many bacteria were there 3 hours after the experiment began?
c) When will the population reach 60?
Click here to see answer by josgarithmetic(39620)

Question 1149659: Assessment Tool
Data for the number of facebook users can be readily found on the internet. Below is listed facebook user numbers from the years 2004 to 2016. Answer the following questions.
YEAR 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016
1 6 12 58 145 360 608 845 1056 1230 1440 1710 2000
USERS (in millions)
Enter this data into your calculator and view the scatterplot. Use years since 2000 as your independent variable. You can use your calculator to find the answers to any of these questions.
Exponential Model
Logistic Model
a)
Fit both an exponential model and a logistic model to the data; sketch the graphs of those models on the scatter plots above.
b)
Which of the two models above best fits the data? Write the equation of that model.
c)
Based on this model, what will be the predicted number of Facebook users in the year 2025? Include units.
d)
is the value in part (c) a reasonable or unreasonable prediction for the number of Facebook users in 2025? Explain
why or why not.

Click here to see answer by jim_thompson5910(35256)

Question 1149666: Solve for x in the following equations
(i). In x^2+ In x = 9
(ii). e^2x = 5

Click here to see answer by Alan3354(69443)

Question 1149888: A storage tank contains niobium-97m, a radioactive element.the percentage of the element that remains is halved each hour. let p=f(t) be the percentage of niobium-97m that remains at t hours since the element was placed in the tank.
A) find an equation of f
B)what is the p-intercept of the model? what does it mean in this situation?
C) find f(9). what does it mean in this situation?
D) what is the half-life of niobium-97m?

Click here to see answer by greenestamps(13200)

Question 1150071: Find the slope of the line tangent to the following at point where x = 2:
〖f(x)=e〗^(-0.1x^2+2x-3)

Click here to see answer by Alan3354(69443)

Question 1150248: Hopefully simple question that I just can't find the answer to...
I have y=ax^b. I know y, a, and b, I want to solve for x.
Thank you!
Click here to see answer by ikleyn(52800)

Question 1150454: The first recorded population of a particular country was 30 million, and the population was recorded as 41 million 15 years later. The exponential growth function A=30e^k*t describes the population of this country t years later since the first recording. Use the fact that 15 years later the population increased by 11 million to find k to three decimal places.
Click here to see answer by Cromlix(4381)

Question 1151357: The population of a certain species of a fish has a relative growth rate of 1.2% per year. It is estimated that the population in the year 2000 was 10 million.

If the fish population has reached about 13 million how many years have passed?
The equation is N(t)=Ne^rt
Click here to see answer by josmiceli(19441)

Question 1151657: how do I solve something like this?
2^(log(base4)x)
My book says the answer is sqrt(x) but I’m completely lost and can’t find any tips.
Click here to see answer by MathLover1(20850)

Question 1151658: 2^(log(base4)x)
My book says the answer is sqrt(x). Any explanation would be great.
Click here to see answer by math_helper(2461)

Question 1151694: 25^(log(base5)(3x^2))
Is the answer 9x^4? If not can you show the the steps?
Click here to see answer by greenestamps(13200)

Question 1151697: log(base4)(2(e^x)(sinx))
Could you show me the steps worked out?
Click here to see answer by MathLover1(20850)

Question 1151708: log(base4)2^((e^x)(sinx))
Could you show me the steps worked out please.
Click here to see answer by josmiceli(19441)

Question 1151721: 25^(log[base5](3x^2))
Click here to see answer by MathLover1(20850)

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