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 1187968: 7. Suppose that the total profit in hundreds of dollars from selling x items is given by P(x) = 4x^2 - 5x + 10. Find the marginal profit at x = 5. show Full working.
Click here to see answer by Solver92311(821)

Question 1188014: The function f(x)=20(0.975)^x models the percentage of the surface sunlight, f(x), that reaches a depth of x feet beneath the surface of the ocean. Use the function f(x) to algebraically determine the depth, to the nearest hundredths of the foot, there is a 10% of surface sunlight. Use logarithms.
Click here to see answer by ikleyn(52800)

Question 1188013: The function f(x)=20(0.975)^x models the percentage of the surface sunlight, f(x), that reaches a depth of x feet beneath the surface of the ocean. What percent is the surface sunlight at the ocean level?
Click here to see answer by ikleyn(52800)

Question 1187768: Use logarithmic differentiation to find the derivative of the function.
y=x^−8/x
y′=

Click here to see answer by greenestamps(13200)

Question 1187768: Use logarithmic differentiation to find the derivative of the function.
y=x^−8/x
y′=

Click here to see answer by AnlytcPhil(1806)

Question 1188264: You bought a new Honda Accord in April 2018 for $24,500. The car has depreciated at a continuous rate of 13% annually. Now, you want to buy a different car, so it's time to sell your Honda.
What is the value of the car, to the nearest hundred dollars, in April 2021?
Your neighbor offers you $17,000 to buy your Honda. Is it a good deal? Should you take his offer?

Click here to see answer by Alan3354(69443)

Question 1188332: Without using tables, show that log base 10 of 19 is approximately equal to (2log base 10 of 6 + 1).
Click here to see answer by ikleyn(52800)

Question 1188333: Without using tables, show that log base 10 of 17 is approximately equal to (2log base 10 of 6 + 3log base 10 of 2).
Click here to see answer by ikleyn(52800)

Question 1188333: Without using tables, show that log base 10 of 17 is approximately equal to (2log base 10 of 6 + 3log base 10 of 2).
Click here to see answer by Alan3354(69443)

Question 1188339: A scientist has started his experiment with 5,000,000 cells. He noticed that 45% of the cells die every minute. How long does it take for the number of cells to be less than 1,000?
Click here to see answer by Theo(13342)

Question 1188703: Express given logarithm in terms of a and b:
if , , then is?
Click here to see answer by greenestamps(13200)

Question 1188720: A culture of bacteria triples every 8 hours. if there are 100 bacteria now, and 2700 bacteria after 24 hours, find the bacteria population 2 hours earlier
Click here to see answer by Solver92311(821)

Question 1188792: 1. If 6^x = 5, what does 6^-2x equal?
2. if 7^x=3, what does 7^-2x equal?
Click here to see answer by ikleyn(52800)

Question 1188809: Determine if the statement is true or false. If statement is false, make the necessary change(s) to produce a true statement.
If f (x) = 2^x then f(a+b)= f(a)+f(b)
Click here to see answer by Alan3354(69443)

Question 1189226: Please explain how to solve this: https://docs.google.com/document/d/1jpqO35zDSlUDFyoB_pZ0TZF8JsOYXjmlSxNh7r31O-s/edit?usp=sharing
Click here to see answer by Boreal(15235)

Question 1189265: Analyze the graph of exponential function (𝑓(𝑥)=a^𝑥) and logarithmic function (𝑔(𝑥)=log 𝑎𝑥) <-- (𝑎 is log base) for 𝑎 =5 on the same coordinate axes. Also, for 𝑎=1/5 analyze both graphs.
Click here to see answer by greenestamps(13200)

Question 1189403: Solve for x,

Click here to see answer by Boreal(15235)

Question 1189542: An initial population of 30 fish is introduced into a lake. This fish population grows according to a continuous exponential growth model. There are 69 fish in the lake after 12 years.
(a) Let “t” be the time (in years) since the initial population is introduced, and let y be the number of fish at time t. Write a formula relating y to t.
Use exact expressions to fill in the missing parts of the formula. Do not use approximations.
(b) How many fish are there 14 years after the initial population is
introduced?
Do not round any intermediate computations, and round your
answer to the nearest whole number.
Click here to see answer by Theo(13342)

Question 1189571: Arjun incorrectly writes log7 x+log7 y-log7 z as a single logarithm.
log7 x + log7 y - log7 z = log7 (x+y=z)
Where did Arjun make errors? Explain his errors and the properties of
logarithms that lead to the correct answer. State the correct answer.

please help, i beg you, please
Click here to see answer by math_tutor2020(3817)

Question 1189626: Hi, I'm really stuck on these two questions, is there any chance I could get some help?? Thanks in advance!

https://drive.google.com/file/d/1VjNtgtaZvxc99w-Ig2_eRBl6guaa_qrw/view?usp=sharing
https://drive.google.com/file/d/1MHiwW4Kn8vAk2o-nxhcYgEd5uUfuUNpn/view?usp=sharing
Click here to see answer by Boreal(15235)

Question 1189963: y=2(1/2)^(x+6) -7
state transformations, then graph the parent function and transformed functions, clearly plotting the KEY points, also draw and label the asymptotes

Click here to see answer by ikleyn(52800)

Question 1190047: A sample of a radioactive substance has an initial mass of 31.9 mg. This substance follows a continuous exponential decay model
and has a half-life of 9 minutes.
(a) Let t be the time (in minutes) since the start of the experiment, and
let y be the amount of the substance at time t.
Write a formula relating y to t.
Use exact expressions to fill in the missing parts of the formula.
Do not use approximations.
(b) How much will be present in 14 minutes?
Do not round any intermediate computations, and round your
answer to the nearest tenth.

Click here to see answer by ikleyn(52800)

Question 1190046: An initial population of 280 fish is introduced into a lake. This fish population grows according to a continuous exponential growth
model. There are 588 fish in the lake after 8 years.
(a) Let t be the time (in years) since the initial population is introduced,
and let y be the number of fish at time t.
Write a formula relating y to t. Use exact expressions to fill in the missing parts of the formula. Do not use approximations.
(b) How many fish are there 19 years after the initial population is
introduced? Do not round any intermediate computations, and round your
answer to the nearest whole number.
Click here to see answer by josgarithmetic(39620)

Question 1190048: The mass of a substance, which follows a continuous exponential growth model, is being studied in a lab. The doubling time for this substance was observed to be 14 days. There were 9.3 mg of the substance present at the beginning of the study.
(a) Let t be the time (in days) since the beginning of the study, and let
y be the amount of the substance at time t.
Write a formula relating y to t.
Use exact expressions to fill in the missing parts of the formula.
Do not use approximations.
(b) How much will be present in 16 days?
Do not round any intermediate computations, and round your
answer to the nearest tenth
Click here to see answer by ikleyn(52800)

Question 1190085: Write an exponential function in the form y=ab^x
that goes through points (0, 12) and (2,768)
Click here to see answer by Theo(13342)

Question 1190085: Write an exponential function in the form y=ab^x
that goes through points (0, 12) and (2,768)
Click here to see answer by ikleyn(52800)

Question 1190101: Write an exponential function in the form y=ab^2 (0,10) and (2,490)
Click here to see answer by ikleyn(52800)

Question 1190861: A bacteria culture starts with 1,200 bacteria. Two hours later there are 1,800 bacteria. Find an exponential model for the size of the culture as a function of time t in hours.
f(t) =
Use the model to predict how many bacteria there will be after 2 days. (Round your answer to the nearest hundred thousand.)
______ bacteria
Click here to see answer by josgarithmetic(39620)

Question 1191503: Compute the simple interest INT for the specified length of time and the future value FV at the end of that time (in dollars). Round all answers to the nearest cent.
$11,800 is invested for 8 months at 11% per year.
INT = $
Incorrect: Your answer is incorrect.
FV = $
Click here to see answer by ikleyn(52800)

Question 1191541: Convert the following:
a. 9F2Ch to binary

Can you please explainb to me the question step-by-step? Thank you!
Click here to see answer by math_tutor2020(3817)

Question 1191545: Find the result of each operation assume A = 11110001 and B = 10101010
a. A AND B
b. A NAND B

This is my last question for the day! Can you explain me the steps of this question and after, I'll do others by myself? Thanks again!
Click here to see answer by math_tutor2020(3817)

Question 1192136: The exponential model (A=863e^0.03t) describes the population, A, of a country in millions, t years after 2003. Use the model to determine the population of the country in 2003.
Click here to see answer by ikleyn(52800)

Question 1192399: Not sure what to do.
The following table represents the number of koala bears alive since the year 2000. Write a function for the koala bear population, P(t), as a function of t, the time in years since 2000.
1(time since 2000)-------------------P(population of koala bears)
0 --------------------------- 100,000
1---------------------------- 93,500
2---------------------------- 87,423
21--------------------------- 24,381

Click here to see answer by ikleyn(52800)

Question 1192786: Suppose you invest $600 into an account that compounds continuously at a rate of 1.75%. How long would you have to leave the money in the account to have an ending balance of $1350?
Click here to see answer by Theo(13342)

Question 1192789: Find a formula for the exponential function that satisfies g(0)=13 and g(-2)=13/6
Click here to see answer by greenestamps(13200)

Question 1192940: A little confused on this question. Johnny invested $500 into a savings account that earns 2.3% interest. If he plans on leaving the money in the account for 10 years and has no intention of adding or withdrawing from it, should he choose the account that is compouneded annually or daily?
Click here to see answer by Boreal(15235)

Question 1192939: If you invest $300 at 2.25% compounded monthly, how many years (to the nearest hundredth) would it take to grow your investment to $1,200?
Click here to see answer by Boreal(15235)

Question 1192949: (1/4)^x+2=66

Click here to see answer by josgarithmetic(39620)

Question 1192956: If you have a logarithmic word problem and you are finding the number of years and the problem says to round your answer to the nearest whole year and you get 8.60 would you round up to 9 years or down to 8 years? Thanks

Click here to see answer by ikleyn(52800)

Question 1192945: Simplify
8m^(1/3)n^(-3/2)(-2m^(-2/3)n^(1/3))^-4
Click here to see answer by MathLover1(20850)

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