Tutors Answer Your Questions about Exponents-negative-and-fractional (FREE)
Question 1183428: Assume there is a certain population of fish in a pond whose growth is described by the logistic equation. It is estimated that the carrying capacity for the pond is 2000 fish. Absent constraints, the population would grow by 210% per year.
If the starting population is given by p0=500, then after one breeding season the population of the pond is given by
p1 =
After two breeding seasons the population of the pond is given by
p2 =
Click here to see answer by Boreal(15235)   |
Question 1191665: Determine a function, I(t), that determines Jennifer’s investment account balance after t
years. For the exponential growth function, what are the “a” and “b” values? What do those values represent? (5 points for the explanation of “a” and “b” and 5 points for the function)
2. Calculate how much money Jennifer will have after 10 years. (10 points)
3. What is Jennifer was able to deposit $100,000 as her initial investment, instead of $50,000.
Write a new function, N(t), to show this change. (3 points) Calculate how much money Jennifer would have after 8 years. (2 points)
Using complete sentences, compare the differences in the functions and the amount of money after 8 years for the two different functions. (5 points)
University of Texas at Austin UT High School 1
4. Graph the function I(t) and identify the y-intercept and the equation of the asymptote. (5 pts)
5. Graph the function N(t) and identify the y-intercept and the equation of the asymptote. (5 pts)
6. What does the asymptote mean in terms of Jennifer’s investment account? Be sure to explain your reasoning for credit. (5 pt)
7. Due to a worldwide recession, Jennifer’s financial advisor informs her the account is no longer growing after 4 years. He recommends she move her money to an account that is more conservative and earns only 4% annually. Determine the amount in Jennifer’s investment account after 4 years(using the $50,000 investment), rounding to the nearest dollar. It may be helpful to create a table. (10 points)
8. Write a new function, N(t), that represents the amount of money in Jennifer’s new account after t years. Be sure to use correct notation. (5 pts)
9. Did the asymptote of the new function change due to Jennifer moving her investment? Explain your reasoning. (5 pts)
Click here to see answer by ikleyn(52831)  |
Question 1195505: A box contains 5 white and 4 blue marbles. Two marbles are drawn from the box in succession without replacement. What is the probability of getting a white on the second draw given that it is white on the first draw?
Click here to see answer by ikleyn(52831) |
Question 1196410: The most common roach in the United States is the German cockroach. In a
year, a home can be infested with about 30,000 cockroaches. About how many
cockroaches would infest a home in one month?
a 2.5 × 10^3
b 2.5 × 10^4
c 3.6 × 10^4
d 3.6 × 10^5
Click here to see answer by ikleyn(52831) |
Question 1196410: The most common roach in the United States is the German cockroach. In a
year, a home can be infested with about 30,000 cockroaches. About how many
cockroaches would infest a home in one month?
a 2.5 × 10^3
b 2.5 × 10^4
c 3.6 × 10^4
d 3.6 × 10^5
Click here to see answer by MathTherapy(10555)  |
Question 1197601: The half life of a certain isotope is 8.5. If we we have a sample of 10 ounces of isotope show much of it will remain after one full day. One of 4 choices is the answer. 0.28 ounces, 0
14 ounces, 1.41 ounces, or 2.83 ounces. Which answer is correct?
Click here to see answer by josgarithmetic(39623) |
Question 1197601: The half life of a certain isotope is 8.5. If we we have a sample of 10 ounces of isotope show much of it will remain after one full day. One of 4 choices is the answer. 0.28 ounces, 0
14 ounces, 1.41 ounces, or 2.83 ounces. Which answer is correct?
Click here to see answer by ikleyn(52831) |
Question 1197601: The half life of a certain isotope is 8.5. If we we have a sample of 10 ounces of isotope show much of it will remain after one full day. One of 4 choices is the answer. 0.28 ounces, 0
14 ounces, 1.41 ounces, or 2.83 ounces. Which answer is correct?
Click here to see answer by greenestamps(13203)  |
Question 1197601: The half life of a certain isotope is 8.5. If we we have a sample of 10 ounces of isotope show much of it will remain after one full day. One of 4 choices is the answer. 0.28 ounces, 0
14 ounces, 1.41 ounces, or 2.83 ounces. Which answer is correct?
Click here to see answer by ewatrrr(24785)  |
Question 1199265: Solve for x.
2x^(2/3) - 5x^(1/3) - 3 = 0
Using the Diamond Method, I got the following:
2x^(2/3) - 6x^(1/3) + x^(1/3) - 3 = 0
I then applied factoring by group.
2x^(1/3)[x^(1/3) - 3]
Setting each factor to 0 and solving for x, I got the following
values: 0, 27
According to the textbook, x = 27 is one of the solutions.
The second value of x should be -1/8.
I did everything I could think of to find the second value of x but to no avail.
How do I find x = -1/8?
Click here to see answer by ikleyn(52831) |
Question 1199795: can you help me on this hehe i need 3 examples of every law of exponents(FIRST TO FOURTH LAW) thank you so much
The Product rule for radicals
root(xy, n) = root(x, n) * root(y, n)
where x and y are nonnegative numbers and n is a counting number.
The Quotient Rule for Radicals:
root(x/y, n) = (root(x, n)/(root(y, n)
where x and y are nonnegative numbers and y=0.
Additional Rule:
root(m) root(n) x = root(mn)x
Laws of Radicals
First Law of Exponents: xm. xn = xm+n
Second Law of Exponents: xm/xn = xm-n; if x = 0 and m>n
Third Law of Exponents: (xm)n = xmn
Fourth Law of Exponents: (xy)m = xmym
Extension of the Second Law of Exponents:
1. The Zero Exponent: x0 = 1; where x = 0.
2. Definition of Negative Exponent: x-n= 1/xn where x = 0 and n is a counting number.
Click here to see answer by Solver92311(821)  |
Question 1201491: Assume there is a certain population of fish in a pond whose growth is described by the logistic equation. It is estimated that the carrying capacity for the pond is 1900 fish. Absent constraints, the population would grow by 210% per year.
If the starting population is given by p0=600
, then after one breeding season the population of the pond is given by
p1=
After two breeding seasons the population of the pond is given by
p2=
Click here to see answer by Glaviolette(140)  |
Question 1206141: Assume there is a certain population of fish in a pond whose growth is described by the logistic equation. It is estimated that the carrying capacity for the pond is 1600 fish. Absent constraints, the population would grow by 120% per year.
If the starting population is given by ,p0=200 then after one breeding season the population of the pond is given by
P1=
after two breeding seasons the population of the pond is given by
P2=
Click here to see answer by ikleyn(52831) |
Question 1175054: Assume there is a certain population of fish in a pond whose growth is described by the logistic equation. It is estimated that the carrying capacity for the pond is 1500 fish. Absent constraints, the population would grow by 200% a year.
If the population is given by po=600, then after one breeding season the population of the pond is given by
p1=
After two breeding seasons the population of the pond is given by
p2=
Click here to see answer by ikleyn(52831) |
Question 1200305: Let’s say you are remodeling your room. You want to determine various measurements using
polynomial expressions. Your room is
8x
feet by
3x
feet.
1. How much border should you purchase is you are putting border around the edge of the top of
your walls? (Assume there is wall space above the opening for the door).
2. On the floor, you will need to purchase wood floor panels. How much should you buy to
cover the entire floor of your bedroom?
3. Your mom just told you that she will give you your sister’s bedroom which as 3 more feet of
length and 2 less feet of width. What is the new amount of border you will need to purchase?
4. In the new room, what is the new amount of flooring you will need to purchase?
5. What is the difference in the size of the new bedroom and the original bedroom?
Click here to see answer by GingerAle(43) |
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