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 1024729: Please help me with these problems. Thanks and show all work
1. A bank features a savings account that has an annual percentage rate of r=4.7
% with interest compounded quarterly. Zach deposits $3,500 into the account.
The account balance can be modeled by the exponential formula S(t)=P(1+rn)nt
, where S is the future value, P is the present value,r is the annual percentage rate, n is the number of times each year that the interest is compounded, and t is the time in years.
(A) What values should be used for P, r, and n?P=, r=, n=

(B) How much money will Zach have in the account in 8 years?
Answer = $ . Round answer to the nearest penny

2.If 15700 dollars is invested at an interest rate of 8 percent per year, find the value of the investment at the end of 5 years for the following compounding methods.
(a) Annual:
Your answer is
(b) Semiannual:
Your answer is
(c) Monthly:
Your answer is
(d) Daily:
Your answer is

3. An unknown radioactive element decays into non-radioactive substances. In 420 days the radioactivity of a sample decreases by 26 percent.
(a) What is the half-life of the element?
half-life: (days)
(b) How long will it take for a sample of 100 mg to decay to 75 mg?
time needed
Click here to see answer by solver91311(24713)

Question 1024921: Suppose f(x) is the following function, defined when x > 0.
f(x) = e^x -3x - x^2
Use Mathcad to help you find the x-coordinate, to 2 decimal places, of the critical point of f(x).
Click here to see answer by Fombitz(32388)

Question 1024916: If a = -61 and x > 0, then what, to 2 decimal places, is the value of the x-coordinate of the critical point of f?
f(x)= ln(x) + x^a
Click here to see answer by Fombitz(32388)

Question 1025009: How to find the inverse of y=log 8(4x-5)
Click here to see answer by Fombitz(32388)

Question 1025186: Please help me the answer I came up with for these problems are 6.9315year. What am I doing wrong.

Find the time it takes for $5,000 to double when invested at an annual interest rate of 1%, compounded continuously.
years
Find the time it takes for $500,000 to double when invested at an annual interest rate of 1%, compounded continuously.
years
Give your answers accurate to 4 decimal places
Click here to see answer by Alan3354(69443)

Question 1025183: Please help me with this every answer I have tried is wrong.
A bacteria culture starts with 1000 bacteria and grows at a rate proportional to its size. After 3 hours there will be 3000 bacteria.
(a) Express the population P after t hours as a function of t.
P(t)=
My answers were 0.366204, P(3)=1000e^0.366204
Click here to see answer by robertb(5830)

Question 1025453: What is the value of 3 to the power 1/2 and how
Click here to see answer by Alan3354(69443)

Question 1025478: hi I need some help please the problem states to solve 4 log( 2x + 1 ) = 12. I think I understand how it simplifies to 8 log (x) + 4 log (-12) = 0 , but I'm not sure if that is the correct answer or not. Thank you for your help.
Click here to see answer by Alan3354(69443)

Question 1025549: 3. The length of a rectangle is 4 feet longer than its width. Express the area of the rectangle in factored form and in standard form.
Factored form:

Standard form:

Click here to see answer by Timnewman(323)

Question 1025938: Rewrite to exponential form and solve for x.
Logx^5.0625=4
I was able to change it to exponential form but wasn't able to solve for x.
X^4=5.0625
Now I need help to solve for x.
Click here to see answer by josgarithmetic(39620)

Question 1025936: Rewirte to exponential form and solve for x.
Logx^4=1/3
I was able to change it to exponential form but I wasn't able to solve for x.
X^1/3=4.

The only thing I need now is the value of x.
Click here to see answer by ankor@dixie-net.com(22740)

Question 1025988: Vanessa bought a car for $20,000 . It is expected to depreciate at a continuous rate. What will be the value of the car in 2 years? Use K - .105. The answer should be $16,212.00 I think but I need to see the how or steps. Thanks.

Click here to see answer by Alan3354(69443)

Question 1026003: Hello, could someone please check these and see if my answers are correct? I am supposed to find the indicated real nth roots of x, if any. And, give my answers in simplest form. 1. n=6, x=-64. *no real nth roots*
2. n=3, x=128. my answer 3sqrt(128) broken down to 4 3sqrt(2).
3. n=10, x=1024. my answer is 2.
4. n=7, x=-8sqrt(2)/2187. my answer is -7sqrt(8sqrt(2)/3.
I appreciate any help! Thanks!
Click here to see answer by Fombitz(32388)

Question 1026119: Choose and exponential function that represents a real-world situation and graph the function. Analyze the graph.
Click here to see answer by rothauserc(4718)

Question 1026434: The mass, m (g), of a radioactive sample of sodium decreases from an initial mass of 660 g by 5% each hour. Which range includes the mass of the amount of sodium left after 24 hours?
530-550 grams
510-530 grams
180-200 grams
50-70 grams
Click here to see answer by robertb(5830)

Question 1026549: Could someone please check my work on the following paragraph proof? This is to show why 11^1/n must equal n(sqrt)11 to uphold the properties of exponents, fill in the blanks to complete the paragraph proof. The answers I filled in are between ** Suppose b^n=11. Then b is the **nth** root of 11, which is written as **11^1/n**. Now consider that 11=11^1 and that n/n=1. By substitution, 11^1=11^n/n and by the **Power of a Power** property of exponents, 11^n/n=11^(1/n*n)=**(11^1/n)^n**. By the transitive property, since b^n=11 and 11=**(11^1/n)^n**, we know that b^n=**(11^1/n)^n)**. Therefore, b=11^1/n and as previously shown b=**n(sqrt)11**. Thus, **n(sqrt)11=11^1/n** Sorry it's so long, but I would appreciate any help!
Click here to see answer by robertb(5830)

Question 1026585: log9^-1 + xlog(3^(5x-7))^(1/3) = 0 Find the exact value of x. Thanks!
Click here to see answer by stanbon(75887)

Question 1026745: Would someone please check my work? The question is which of the following statements does NOT accurately describe an account into which $400 is deposited and earns 6% annual interest compounded quarterly?
A. 400(1.015)^4t
B. 400(1+.06/4)^4t
C. 400(1.06/4)^4t
D. none of these (all are accurate)
I chose C as being incorrect. Am I correct? Thanks in advance!
Click here to see answer by josgarithmetic(39620)

Question 1026743: Could someone please check my work? I am supposed to circle all true statements about f(x)=-1/2*3^x+1-2.
A. The graph has a horizontal asymptote at y=-2.
B. The domain is all real numbers.
C. The range is y>2.
D. The graph crosses the y-axis at -5/2.
E. The graph never crosses the x-axis.
F. The growth factor is -3.
I believe B and E are true and I'm not sure about A??? Thanks for any help!
Click here to see answer by ikleyn(52800)

Question 1026874: Hello, could someone please help me with a two part problem writing equations? The problem states: Houses in Madison's town are losing 11% of their value each year. Let v be the current value of Madison's house. Write an equation that describes the projected value, p, at a time, t, years from now. I have P=V(1-r)^t and after substituting 11 for r, I got the equation P=V(0.89)^t. Then, the next part states "Rewrite your equation to find the effective monthly percentage decrease in value". I thought it might be V=(1-0.11/12)^12t, but I'm not sure. Any help would be appreciated!
Click here to see answer by josgarithmetic(39620)

Question 1026998: We are currently working on logarithmic functions, and we are given two equations that need to be solved, but I find it somewhat difficult to reach to a logical solution.
i: 4*ln*(2x-1)-ln*9=2*ln*(x-1)+2*ln*(x+1)
ii:log*(2x-5)+log*(3x+7)=4*log*2

Click here to see answer by josgarithmetic(39620)

Question 1027007: A penny is 1.55 mm thick. Imagine that you stack pennies on top of each other every day. Each day, you double the amount of pennies in the stack. This means that on day 0, there is 1 penny. On day 1, there are 2 pennies. On day 2, there are 4 pennies, etc.
If this pattern continues, in how many days will the stack of pennies be about 1 meter tall?
Also, the distance from the earth to the moon is 405,696,000 meters. About how many stacked
pennies would it take to reach the moon? Round to the nearest hundredth. After about how many days will the stack of pennies be tall enough to reach the moon?
Thanks!
Click here to see answer by mathmate(429)

Question 1027006: Imagine that you stack pennies on top of each other every day. Each day, you double the amount of pennies in the stack. This means that on day 0, there is 1 penny. On day 1, there are 2 pennies. On day 2, there are 4 pennies, etc. What exponential function is being modeled here? If this pattern continues, in how many days will the stack of pennies be about 1 meter tall? BTW the pennies are 1.55 mm's thick
Click here to see answer by josmiceli(19441)

Question 1027196: Logx_log10=14
Click here to see answer by Alan3354(69443)

Question 1027319: Hi, I'm having trouble solving and figuring what to do for this problem:
Solve 5^x+2 = 12
Thank you.
Click here to see answer by josgarithmetic(39620)

Question 1027427: I am having issues with word problems, just not sure how to set them up and then complete.
Radioactive carbon-14 decays according to the function Q(t)=Q0e^-0.000121t where t is time in years, Q(t) is the quantity remaining at time t, and Q0 is the amount present at t=0. Estimate the age of bone fragment if 17% of the original quantity of carbon-14 remains.
Thank you for all your help.
Click here to see answer by josmiceli(19441)

Question 1027424: hey I am having some issues trying to layout this word problem and could use some help please.
A population of 1000 bacteria is growing exponentially and doubles in number every 17 mins. How long until there are 3600 bacteria?
it then asks to show hand work using algebra and either a common log or natural log. I am confused on what to do.
Thanks for all your help.
Click here to see answer by josgarithmetic(39620)

Question 1027571: Using the formula
y=ae^bx
I want to change the equation so I can find x when y is known?
Click here to see answer by Fombitz(32388)

Question 1026716: P=Po (1/2)^h/4795
Click here to see answer by fractalier(6550)

Question 1027617: Determine which is greater without a calculator.
log17 to the base 4, or log 24 to the base 5
Click here to see answer by fractalier(6550)

Question 1027741: I can't remember how to solve for these types of problems
2log x + log11 (I think I have to use the power property)
Log 2^11 = 3.31 ?
Click here to see answer by josmiceli(19441)

Question 1027837: Graph
y=2^(x-3)-1 [so 2 to the power of x-3.]
I'm wondering how to set up the graphing on this.
Click here to see answer by josgarithmetic(39620)

Question 1027952: Animal populations are not capable of unrestricted growth because of limited habitat and food supplies. Under such conditions the population growth follows a logistic growth model.
p(t)=d/1+ke^-ct
where c,d,and k are positive constants. For a certain fish population in a small pond d= 1200, k= 11, c = 0.2, and t is measured in years. The fish were introduced into the pond at time = 0.
a)
How many fish were originally put into the pond?
b)
Find the population of fish
after 10, 20, and 30 years.
c)
Evaluate P(t) for large values of t. What value does the population approach as
t→∞?
Click here to see answer by Theo(13342)

Question 1028046: Please solve log3 x=9
Click here to see answer by Cromlix(4381)

Question 1028215: Pove That The Integral Of Secx =ln/secx +tanx/
Click here to see answer by Alan3354(69443)

Question 1028253: For a student recreation building at Northland Community College, an
architect wants to lay out a rectangular piece of land that has a perimeter
of 204 m and an area of 2565 m2
. Find the dimensions of the land (Hint:
write a system of two equations, then solve the system)
Click here to see answer by Theo(13342)

Question 1028423: I'm not sure if this is the right place for this question, but it seemed the most appropriate.
What is the limit of 2(x^2)(e^x) as x approaches negative infinity.
Technically this is a calculus question, but what I'm more interested in is how to manipulate the given equation. Apparently, (x^2)(e^x) can be rewritten as (x^2)/(e^(-x)). I understand the use of reciprocals and conjugates, but how can someone just flip one part of the equation like that?

Click here to see answer by fractalier(6550)

Question 1028516: how would you solve the equation e^4x-1 -3=12?
Click here to see answer by josmiceli(19441)

Question 1028567: The number of bacteria present in a culture after "t" hours is given by the formula Q(t) - Q0(meaning sub zero)e^0.3t Q (sub zero) = initial bacteria
If 6,640 bacteria are present after 4 hours, how many were present initially?
I can't seem to get the formula to work right.
Click here to see answer by rothauserc(4718)

Question 1028620: List all of the possible numbers of intersection points for the following
systems (it might help to draw a picture):
A) A line and a parabola.
B) Two parabolas.
C) A parabola and an ellipse.
D) An ellipse and a hyperbola.
Click here to see answer by Fombitz(32388)

Question 1028685: How would you solve this 4/x-1 =x+1/12 (4 is supposed to be on top of x-1 in fraction form and so is x+1 over 12)
Click here to see answer by rothauserc(4718)

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