After a devastating winter, when thousands of fish died, an environmental scientist has replenished the trout stock in a fishing pond. He started with 5,000 baby trout and has finished a count to find that, in 4 years, the population is estimated to be 8,500. Assuming an exponential growth pattern, what is the annual growth rate (rounded to the nearest tenth of a percent) of the new trout population?
The annual growth rate of the new trout population is approximately 12.0%.
Explanation:To find the annual growth rate of the trout population, we can use the exponential growth formula:
P = P0ert
where P is the final population, P0 is the initial population, r is the annual growth rate, and t is the number of years.
In this case, we have P = 8,500, P0 = 5,000, and t = 4. Plugging these values into the formula, we can solve for r:
8,500 = 5,000e4r
Divide both sides by 5,000:
1.7 = e4r
Take the natural logarithm of both sides:
ln(1.7) = 4r
Divide both sides by 4:
r ≈ ln(1.7)/4 ≈ 0.120
Final answer:
The annual growth rate of the trout population is calculated using the formula for exponential growth. By substituting the given values into the formula, the growth rate is determined to be approximately 13.41% per year. After rounding, the annual growth rate is 13.4%.
Explanation:
To calculate the annual growth rate of the trout population, we can use the formula for exponential growth, which is P = P0e(rt), where:
P is the final population size,
P0 is the initial population size,
r is the annual growth rate,
t is the time in years.
We know that P0 = 5,000 (initial population), P = 8,500 (final population), and t = 4 years. To find r, we rearrange the formula to solve for r:
r = (ln(P/P0)) / t
Plugging in the values gives us:
r = (ln(8500/5000)) / 4 = ln(1.7) / 4 ≈ 0.1341 or 13.41% per year
Rounding to the nearest tenth of a percent, the annual growth rate is 13.4%.
Why is the polynomial, 4x^2y + 5xy classified as a 3rd degree binomial?
name the property the equation illustrate -5+(8+10)=(-5+8)+10
Find the quotient of 9 divided by 5/8 .
9 / 5/8 =
9/1 / 5/8 =
9/1 * 8/5 = 72/5 = 14 2/5
9. Jane has a checkbook balance of $68.00. She then writes two checks, one for $5.00 and one for $62.50. She also deposits $75.00. She then uses her calculator to determine her new balance. Which of the following is the correct series of keys she should press? A. [ON/C] [68] [+] [75] [=] [5] [=] [62.50] [=] B. [68] [+] [75] [–] [62.50] [–] [5] [=] C. [ON/C] [68] [–] [5] [–] [62.50] [+] [75] [=] D. [68] [+] [75] [–] [5] [–] [62.50] [=]
it is C
she turns the calculator on, then enters her starting balance them subtracts both checks she wrote then added the deposit.
NEED HELP FAST!
6.
(08.02 MC)
Which graph best represents the solution to the following pair of equations?
y = 4x + 2
y = x + 5 (1 point)
How many numbers between 1 and 100 are multiples of both 2 and 7
There are 7 numbers between 1 and 100 that are multiples of both 2 and 7.
Explanation:To find the numbers between 1 and 100 that are multiples of both 2 and 7, we need to find the common multiples of these two numbers. The multiples of 2 are 2, 4, 6, 8, 10, and so on. The multiples of 7 are 7, 14, 21, 28, and so on.
We can see that the common multiples of 2 and 7 are 14, 28, 42, 56, 70, 84, and 98. There are a total of 7 numbers between 1 and 100 that are multiples of both 2 and 7.
Learn more about Multiples of 2 and 7 here:https://brainly.com/question/34357814
#SPj3
Which statement could be used to explain why f(x) = 2x – 3 has an inverse relation that is a function?
Answer:
f(x) is a one to one function
Step-by-step explanation:
Frankie purchases a 3 1/2 pound bag of chicken.he uses 1 1/3 of chicken for fajitas how many pounds of chicken are left?
Restaurant sales totaled 38,676 for the week. Your customer count was 7,325. What did the average customer spend for the week
divide total by number of customers
38,676/7,325 = 5.28
average was $5.28
Frank kicks a soccer ball off the ground and in the air, with an initial velocity of 30 feet per second. Using the formula H(t) = −16t2 + vt + s, what is the maximum height the soccer ball reaches? 14.1 feet 13.7 feet 13.2 feet 15.2 feet
The answer is A or 14.1!
how to factorise x squared minus 16
you can buy 3 apples at quick market for $1.17, you can buy 5 of the same apples at Stop and Save for $2.40.
a.Which store is the better buy?
b. How much will you save per apple if you purchase it from the cheaper store?
For which value or values are the expressions 15k + 9 and 3(2k + 3) + 9k equivalent? A) no values B) 3 C) 3,5 and 8 or D) all values
Final answer:
The expressions 15k + 9 and 3(2k + 3) + 9k are equivalent for all values of k because after simplifying the second expression, it matches the first expression exactly.
Explanation:
To determine for which value or values the expressions 15k + 9 and 3(2k + 3) + 9k are equivalent, we must first simplify the second expression.
Simplify 3(2k + 3) + 9k:
= 6k + 9 + 9k
= 15k + 9.
Now we compare the simplified forms of both expressions. It is clear that they are identical in form, meaning that they are equivalent for all values of k. No additional values are needed; the expressions are universally equivalent as they simplify to the same equation.
Anna took Allie out for lunch their lunches cost $13.28 and $14.25 including tax and tip and a paid with $40 how much change did Anna receive
write general rule for adding
a. two integers with the same sign.
b. two integers with different signs.
c. two integers that vary in sign.
When adding integers, if the signs are the same, add the numbers and keep the sign. If the signs are different, subtract the smaller number from the larger number, using the sign of the larger number.
Explanation:To offer some general rules for adding integers, consider the following scenarios:
When we add two integers with the same sign, we add the absolute values of the numbers and keep the common sign. For example, (-4) + (-3) equates to -7, as they are both negative. If we are combining two integers with different signs, we subtract the smaller number from the larger number and use the sign of the larger number. For instance, 7 + (-2) equals 5, because 7 is larger and positive. When adding two integers that vary in sign, it suggests that one number could be positive and the other negative or vice-versa. Thus, we follow the second rule mentioned above. For example, -6 + 3 gives -3 because 6 is bigger and negative. Learn more about Adding Integers here:
https://brainly.com/question/27908445
#SPJ12
The equation shows the relationship between x and y: y = 6x + 1 What is the slope of the equation?
Sergei says that 10%
of a number will always be less than 20%
of any other number.
Complete one inequality to support Sergei's claim and one to show that he is incorrect.
10% of 100 < 20% of 200.
10% of 1000 > 20% of 100.
What are the numbers that make the claims correct?Percentage is the fraction out of an amount that is usually expressed as a number out of hundred. Percentages are a measure of frequency. The sign used to represent percentages is %.
To learn more about percentages, please check: https://brainly.com/question/25764815
#SPJ2
Consider 8x2 - 48x = -104. Write the equation so that a = 1
Answer:
x² + (-6x) = -13
ALSO the second answer,
x² + (-6x) __ = -13 + __
Both blanks are 9
Third answer, factor the trinomial and simplify:
(x + -3 )²= -4
Use the square root property of equality to solve
(x – 3)2 = –4.
The solutions are
The correct option is C. 3 ± 2i.
:D
The equation 8x² - 48x = -104 can be rewritten with 'a' = 1 by dividing all terms by 8 and rearranging to the form ax² + bx + c = 0, yielding x² - 6x + 13 = 0.
Explanation:To rewrite the equation so that 'a' = 1, it would be useful to adjust the coefficients in your equation first. Starting with the given equation: 8x² - 48x = -104. We can divide all terms by 8 to normalize the 'a' coefficient.
Doing that gives us: x² - 6x = -13. Now, to write the equation in the form ax² + bx + c = 0, we can add 13 to both sides which results in: x² - 6x + 13 = 0. Now your equation is in the standard quadratic form with 'a' = 1.
https://brainly.com/question/30098550
#SPJ2
How many solutions are there for the system of equations shown on the graph?
No solution
One solution
Two solutions
Infinitely many solutions
Help best answer gets brainliest
!!!!!
John paid $50 for renting a cycle for 5 hours. Which graph shows the relationship between the cost of renting a cycle for different hours?
Answer:
for ever 1 hour the price goes up by ten
Step-by-step explanation:
In a set of integers between 18 and 95, inclusive, how many are divisible by 6 but not 12?
a jar of 25 lollipops in a clinic has 7 that are grape, 10 cherry, and 8 orange. If a nurse selects 4 lollipops randomly, what is the probability that they will all be grape?
how do you find the sum of all integers between square root of 12 + square root of 40?
The diameter of the moon is 2155 miles. Find volume of the moon. Round answers to the nearest whole number and leave pi in the answer
Answer: [tex]1667978979\pi[/tex] cubic miles
Step-by-step explanation:
We know that the shape of moon is sphere.
The volume of sphere is given by :-
[tex]\text{V}=\dfrac{4}{3}\pi r^3[/tex], where r is the radius of sphere.
Given : The diameter of moon = 2155 miles
Then the radius of moon=[tex]\dfrac{2155}{2}[/tex]
Then , the volume of moon is given by :-
[tex]\text{V}=\dfrac{4}{3}\pi (\dfrac{2155}{2})^3=1667978979.2\pi\approx1667978979\pi \text{ cubic miles}[/tex]
Select each quadrilateral that has exactly four right angles.
trapezoid
isosceles
trapezoid
parallelogram
rhombus
rectangle
Answer:
Square, and Rectangle
Step-by-step explanation:
the others don't have a 90 degree angle
What is 74 divided by 3
The value is 24 1/3
How to determine the valueFirst, we need to know that division is an arithmetic operation that is the result of a divisor and a dividend
We have other arithmetic operations, such as;
AdditionSubtractionMultiplicationDivisionBracketparenthesesFrom the information given, we have that;
74 divided by 3
This is represented as;
74/3
Divide the values
24 1/3
Learn about division at: https://brainly.com/question/25289437
#SPJ6
HELP I'M BEING TIMED FOR THIS TEST!!!
Which applies the power of a product rule to simplify (5t)^3?
A. (5t)^3 =5t^3
B. (5t)^3 = 3(5t) = 15t
C. (5t)^3 = 5^3 t^3 = 125t^3
D. (5t)^3 = 5^3t = 125t
Which number line represents all of the values of x for the equation x2 = 16? A number line is shown from negative 10 to 0 to positive 10. There are increments of 2 on the number line, and all these are increments are labeled. A dot is shown on positive 4 and is labeled as p. A number line is shown from negative 10 to 0 to positive 10. There are increments of 2 on the number line, and all these are increments are labeled. A dot is shown on positive 8 and is labeled as p. A number line is shown from negative 10 to 0 to positive 10. There are increments of 2 on the number line, and all these are increments are labeled. A dot is shown on positive 4, another dot is shown on negative 4, and are labeled as p and q, respectively. A number line is shown from negative 10 to 0 to positive 10. There are increments of 2 on the number line, and all these are increments are labeled. A dot is shown on positive 8, another dot is shown on negative 8, and are labeled as p and q, respectively.
Answer: Its the 3rd choice.
You are a member of a darts team and they have won $1750 prize money in a competition. $70 is to be saved for a celebration party; the remainder is to be divided equally between the 14 team members