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 1169252: The count in a bateria culture was 400 after 10 minutes and 1200 after 30 minutes. Assuming the count grows exponentially,
What was the initial size of the culture?

Find the doubling period.

Find the population after 80 minutes.

When will the population reach 14000.
Click here to see answer by Theo(13342)

Question 1169367: 6 2/9 h = 7 5/7
Click here to see answer by Boreal(15235)

Question 1169664: Find the units digit of the sum,$$ 1! + 2! + 3! + \cdots + 2006!. $$(latex)
Find the units digit of the sum, 1! + 2! + 3! + ... + 2006!.(not latex)
I am stuck. I cannot find a pattern because of the high numbers that this problem goes to. I have spent a lot of time, but haven't got anything. Thank you.
Click here to see answer by ikleyn(52800)

Question 1169677: Please help me solve this problem
A researcher is investigating a specimen of bacteria. She finds that the 1000 bacteria grew o 2,048,000 in 60 hours. How fast does the bacteria (a) double? (b) quadruple?
Click here to see answer by ikleyn(52800)

Question 1169777: Log(2x^4y)
Click here to see answer by MathLover1(20850)

Question 1169899: Two investments totaling $33,000 produce an annual income of $2200. One investment yields 8% per year, while the other yields 6% per year. How much is invested at each rate?
Click here to see answer by ikleyn(52800)

Question 1170146: log2 (x + 1) + log2 (3.c - 5) = log2 (5x - 3) +2
Click here to see answer by ikleyn(52800)

Question 1170142: 2. log25 2 + log25 (25 - 4x) = 0.5
Click here to see answer by MathLover1(20850)

Question 1170223: Php 10, 000 is invested at 2% compounded annually. What is the exponential model for this situation?
Click here to see answer by ikleyn(52800)

Question 1170594: At time t=0, 480 grams of an isotope with a half-life of 30 hours is present. How much will have elapsed when only 15 grams remain?
Click here to see answer by ikleyn(52800)

Question 1170597: The population (in millions) of a certain country follows the exponential growth model f(t)=14.2e^{0.018t}, t years after 1994. Predict the population in the year 2020.
Click here to see answer by ikleyn(52800)

Question 1170596: You take out Php 20,000 loan at a 5% interest rate compounded annually. How much will you owe after 10 years?
Click here to see answer by Theo(13342)

Question 1170595: Xian opened a savings account and put Php 6,250 in it. Each year, the account increases by 20%. How many years will it take the account to reach Php 12,960?
Click here to see answer by Theo(13342)

Question 1170776: A bacteria culture contains 1500 bacteria initially and doubles every hour.
(a) Find a function N that models the number of bacteria after t hours.
N(t) =

(b) Find the number of bacteria after 24 hours.
bacteria
Click here to see answer by Solver92311(821)

Question 1170775: If $10,000 is invested at an interest rate of 4% per year, compounded semiannually, find the value of the investment after the given number of years. (Round your answers to the nearest cent.)
(a) 6 years
$

(b) 12 years
$

(c) 18 years
$

Click here to see answer by Solver92311(821)

Question 1170838: A graphing calculator is recommended.
For a certain type of tree, the diameter D (in feet) depends on the tree's age t (in years) according to the logistic growth model
D(t)= 5.4/1+2.9e^-0.01t
Find the diameter of a 24-year-old tree. (Round your answer to three decimal places.)
ft
Click here to see answer by Theo(13342)

Question 1170843: Some biologists model the number of species S in a fixed area A (such as an island) by the species-area relationship
log(S) = log(c) + k log(A)
where c and k are positive constants that depend on the type of species and habitat.
(a) Solve the equation for S.
S =

(b) Using part (a), if k = 2 and the area is doubled, then by what magnitude is the number of species increased?
Click here to see answer by math_tutor2020(3817)

Question 1171025: At time t=0, 500 bacteria are in a petri dish, and this amount triples every 15 days.Give the exponential model.
Click here to see answer by josgarithmetic(39620)

Question 1171054: The magnitude of an earthquake in san Luis Aurora province in May 2020 is 5.4. And it is predicted that there will be another earthquake that will strike somewhere in the philippines that is 5 times stronger than the mentioned earthquake. What could be the possible magnitude of the predicted earthquake? (Use Earthquake magnitude on a Richter scale R=2/3logE/10^4.40
Click here to see answer by Theo(13342)

Question 1171285: Bacteria in a bottle are tripling every minute. If the number of bacteria in the bottle at 7:30 a.m. is 1
1, how many bacteria are in the bottle at 7:44 a.m.?
Click here to see answer by ikleyn(52800)

Question 1171305: The population of germs on a toilet seat doubles every 15 mins. How long to the nearest minute, would it take for the population to triple

Click here to see answer by Edwin McCravy(20059)

Question 1171524: The population is decreasing at a rate of 5% per year. If the population is 28,400 today, what will the population be in 8 years? Round your answer to the nearest whole number, if necessary
Click here to see answer by greenestamps(13200)

Question 1171697: A certain pain reliever has a half-life of 16 hours. If the initial plasma level of this pain reliever, given as a single dose, is 512mg/L, how long will it take for the plasma level to fall to 16mg/L?
Click here to see answer by Theo(13342)

Question 1171696: Paracetamol is a drug used to treat mild to moderate pain and to reduce fever. It has a half-life in the body of 3 hours. Under a Doctor's care, patient N is given a dose of a certain paracetamol. Patient N asks the doctor for another same dose of this paracetamol. The doctor agrees to allow patient N to take dose once there is only 6.25% of the original dose remaining in the body. How long will patient N have to wait, before taking another dose of this paracetamol?
Click here to see answer by Theo(13342)

Question 1171695: Coffee contains caffeine. The half-life of caffeine is 5 hours. This means the amount of caffeine in your bloodstream is reduced by 50% every 5 hours. Suppose you drink a cup of coffee that contains 320 mg of caffeine. How long will it take until there is 5 mg of caffeine left in your bloodstream?
Click here to see answer by Boreal(15235)

Question 1171489: find the co ordinate turning point on the curve y=2e^4x +8e^-4x and determined the nature of the turning point
Click here to see answer by Boreal(15235)

Question 1171939: Write an exponential function in the form y=a•b^x that goes through points (0,7) and (5,1701).
Click here to see answer by Boreal(15235)

Question 1171982: I am missing (or got a block for !) some very basic knowledge of exponents.
Question: X^(-2/3) = (1/9), solve for x
What I did: Raise the power of both L and R to -3/2 in order to get rid of the exponent of the variable X. Then the equation is
X^(-2/3)^(-3/2) = (1/9)^(-3/2) and it solves to X = +/- 27. Book says I got the right answer.
But it says while going through initial step of X^(-2/3)^(-3/2) = (1/9)^(-3/2)
it wants me to add a +/- in front of the (1/9) as
X^(-2/3)^(-3/2) = +/-(1/9)^(-3/2)
Why do I have to insert the +/- sign at this stage. Is it an accepted practice that you add +/- whenever you raise the power a negative fraction?....since it is going to require it anyway further down the steps?
Please help
Thank you
Click here to see answer by math_helper(2461)

Question 1172222: Write an exponential function in the form y=ab^x that goes through points (0, 20) and (8, 5120).

Click here to see answer by Boreal(15235)

Question 1172591: The half-life of Zn-71 is 2.45 minutes. At t=0, there were y⁰ grams of Zn-71, but only 1/256 of this amount remains after some time. How much time(t) has passed?
Click here to see answer by ikleyn(52800)

Question 1172590: The half-life of Zn-71 is 2.45 minutes. Initially, there were y⁰ grams of Zn-71, but only 1/256 of this amount remains after some time. How much time has passed?
Click here to see answer by ikleyn(52800)

Question 1172589: The half-life of Zn-71 is 2.45 minutes. Initially, there were y⁰ grams of Zn-71, but only 1/256 of this amount remains after some time. How much time has passed?
Click here to see answer by ikleyn(52800)

Question 1172939: What interest rate is needed for $12000 to double after 10 years if compounded
continuously?
Click here to see answer by VFBundy(438)

Question 1173220: find first Derivative Of F(X)
f(x)=sqrt(2(3^x))*log(2x+5)
Click here to see answer by ewatrrr(24785)

Question 1173219: find first Derivative Of F(X)
f(x)=((5x-2)^-3)/(3x-2)
Click here to see answer by Alan3354(69443)

Question 1173506: determine the value of b, c and d if log3(root x^b y^c / w^d ) = 3/2log3(x) + log3(y) - 1/2 log3(w) then show that d=bc-5
pls help me with this problem asap the whole fraction is in the square root for the first log
Click here to see answer by math_helper(2461)

Question 1173959: What is the solution to the equation log⁡〖 (2x+4)〗=2? Round to the nearest hundredth, if necessary.
Click here to see answer by ewatrrr(24785)

Question 1174688: I'm not sure if this ones the right category...
Anyway, for this problem I need to simplify all square roots and answers should not be decimals. Factor or solve the following:
3x⁴+2x²+3=2x⁴-2x²+8
Click here to see answer by MathLover1(20850)

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