A population of rabbits in a lab, p(x), can be modeled by the function p(x)=20(1.014)^x, where x represents the number of days since the population was first counted.
Answers
Answer:
(a) 20 represents the initial population and
1.014 represents 1 + % growth of rabbits each day
(b) Average Rate of change = 0.8
Step-by-step explanation:
P.S - The exact question is -
Given - A population of rabbits in a lab, p(x), can be modeled by
the function p(x)=20(1.014)^x, where x represents the number
of days since the population was first counted.
To find - (a) Explain what 20 and 1.014 represent in the context of
the problem.
(b) Determine, to the nearest tenth, the average rate of
change from day 50 to day 100.
Proof -
(a)
Given that the function p(x) is represented as
[tex]p(x) = 20(1.014)^{x}[/tex]
Here,
20 represents the initial population and
1.014 represents 1 + % growth of rabbits each day
(b)
Given,
[tex]p(x) = 20(1.014)^{x}[/tex]
When x = 50
[tex]p(50) = 20(1.014)^{50}[/tex] = 40.08000 ≈ 40.1
When x = 100
[tex]p(100) = 20(1.014)^{100}[/tex] = 80.32033 ≈ 80.3
Now,
Average Rate of change = [tex]\frac{p(100) - p(50)}{100 - 50}[/tex]
= [tex]\frac{80.3 - 40.1}{50}[/tex]
= [tex]\frac{40.2}{50}[/tex]
= 0.804 ≈ 0.8
⇒Average Rate of change = 0.8
Related Questions
How can you convert the dimesions of the area rug from inches to feet?
Answers
Answer:
1 foot equals 12 inches
Step-by-step explanation:
Answer:
Divide the inches by 12
Step-by-step explanation:
[tex]12 in = 1 ft\\ 1 in =\frac{1}{12} ft\\ x in =\frac{x}{12} ft[/tex]
Find the area of four walls of a room (Assume that there are no doors or windows) if its length 12 m., breadth 10 m. and height 7.5 m. ?
Answers
Answer:
Refer to the attached file
Hope it helps..
Have a great day : )
Which is equivalent to the expression below?
2k + (−3m ) − 6k + 2m
A. −4k + (−2m)
B. −4k + (−m)
C. 4k − 5m
D. 4k − m
Answers
Answer:
−4k + (−m)
Step-by-step explanation:
combined like term:
solve for k: 2k - 6k = -4k
solve for m: -3m + 2m = -1m which is -m
combined together the equation: -4k + -m or it can just be -4k - m
Which decimal is equivalent to 1/3
Answers
Answer:
0.3 with the 3 being repeated
The sum of three numbers is 74 the first number is 6 less than the second the third number is 2 times the second what are the numbers
Answers
Answer:
your answer will be 37 or 3
Fidel has a rare coin worth $550. Each decade, the coin's value increases by %10
Which kind of function best models the relationship between time and the coin's value?
Answers
Answer: Exponential
Step-by-step explanation: I did it in khan
the roof of the clock tower is a square pyramid each side of the base is 16 ft the slant height is 22 ft what is lateral area of the roof
Answers
Answer:
Need more points lang sorry
PLS HELP ASAP IN LIKE 1 MINUTE
A shopping bag contains 18 red potatoes and 12 white potatoes. You choose one potato from the bag without looking. Calculate P(~white potato).
Answers
Answer:
2/5
Step-by-step explanation:
Red potato: 18
White potato: 12
Combined: 30
Probability of white potato:
12/30
2/5
In Circle F, determine the value(s) of x.
Answers
Answer:
since inscribed angle is half of the central angle
x²+22=2(x²+3)
x²+22=2x²+6
22-6=2x²-x²
16=x²
x=√16=±4
determine the value(s) of x=±4
Solve for x:
1
1
-X – 2
32
- 2 = (2 – 6)
2
Answers
Answer:x=-215
Step-by-step explanation: hope this helps!
Neil has been running a tutoring business since 2005. He charges a monthly fee for weekly tutoring sessions and a phone help line. Each year, he has increased his fee by the same amount. The table shows what Neil charged each customer for two given years of his business:
Year Annual Tutoring Fee
2005 $1200
2008 $1350
A. What is the rate of change and initial value for Neil’s business? How do you know?
B. Write an equation in slope-intercept form to represent the fees that Neil charges each year.
Answers
Answer:
The answer is 2550
Step-by-step explanation:
Add 1200 and 1350 it'll give you 2550
Answer:
250
2550
Step-by-step explanation:
sorry if wrong but I think
A=250
B=2550
find the value of given expression
[tex] \sqrt{230 - 5} [/tex]
Answers
Answer:
i think it is 345 but not sure
Step-by-step explanation:
Calculate the commission amount for the sale.
7% commission on a $2,560 sale
Answers
Answer:
$179.2
Step-by-step explanation:
7% of 2,560 is 179.2
10^6 times 10^5 as a power of ten - thanks !
Answers
Answer:
one hundred billion
Step-by-step explanation:
10^6 x 10^5 = 10^11
10^11 = 100,000,000,000 or one hundred billion
I hope that's what you meant ^-^
What is the perimeter of ABCD?
14 units
38 units
44 units
49 units
ANSWER: C) 44 units
Answers
[tex]45=9^{\sqrt{x} }[/tex]
Solving Exponential equations using logs. Round any decimal answers to the hundredths
Answers
Answer:
Step-by-step explanation:
a= b^c << === >> logb(a) = c
a b c
Convert 45 = 9^√x << === >> log9 (45) = √x
1.7324867604 = √x
3.0 = x squared both sides
I used a log calculator on the internet when a Gaggled log calculators
A pipe is tested during a 6-hour leak test on 600 feet of 6-inch-diameter plastic pipe with a test pressure of 150 pounds per square inch (psi). The pipes are 10 feet long. During the 6-hour test period, 8 gallons of water were added to maintain the 150 psi pressure. What is the actual leakage from this section of pipe in gallons per hour per 100 joints?
Answers
Answer:
Gil the rule of induced in a test tube videos were
Step-by-step explanation:
hddhfjfjfjjcjccjmvgkkgjfdhfjkghl gmglgkgmglgm GGG of the rule used to the cultivation the
what's the answer to this pls I'll give brainliest
Answers
Answer:
41 the answer is 41 :)
Step-by-step explanation:
What is the distance between the points (-4,5) and (8,9)
Answers
Can somebody please help me out with this question? Asap
Answers
A. Simplify x + 8 to 8x.
Write the equation of the line that is perpendicular to y = -2/3 x +2 and goes through the point (-1, 4). Make sure your final answer is in slope-intercept form
Answers
Given:
The equation of a line is
[tex]y=-\dfrac{2}{3}x+2[/tex] ...(i)
The perpendicular line passes through the point (-1,4).
To find:
The equation of the perpendicular line.
Solution:
The slope intercept form of a line is:
[tex]y=mx+b[/tex] ...(ii)
Where, m is the slope and b is the y-intercept.
On comparing (i) and (ii), we get
[tex]m=-\dfrac{2}{3}[/tex]
Product of slopes of two perpendicular lines is -1.
Let the slope of perpendicular line is [tex]m_1[/tex].
[tex]m\times m_1=-1[/tex]
[tex]-\dfrac{2}{3}\times m_1=-1[/tex]
[tex]m_1=\dfrac{3}{2}[/tex]
The slope of the perpendicular line is [tex]m_1=\dfrac{3}{2}[/tex] and it passes through the point (-1,4). So, the equation of the line is:
[tex]y-y_1=m_1(x-x_1)[/tex]
[tex]y-4=\dfrac{3}{2}(x-(-1))[/tex]
[tex]y-4=\dfrac{3}{2}(x+1)[/tex]
[tex]y-4=\dfrac{3}{2}x+\dfrac{3}{2}[/tex]
Add 4 on both sides.
[tex]y-4+4=\dfrac{3}{2}x+\dfrac{3}{2}+4[/tex]
[tex]y=\dfrac{3}{2}x+\dfrac{3+8}{2}[/tex]
[tex]y=\dfrac{3}{2}x+\dfrac{11}{2}[/tex]
Therefore, the equation of required line is [tex]y=\dfrac{3}{2}x+\dfrac{11}{2}[/tex].
A 8 foot length of 4 inch wide crown molding costs $15. How much will it cost to buy 38 feet of crown molding?
Answers
Answer:
$71.25
Step-by-step explanation:
cost of one feet of molding = $15/8 = $1.875
Cost of 38 feet of crown molding = $1.875 x 38 = $71.25
Ed wants to bicycle at least 75 miles this week. The inequality 11 + 4b > 75 can be used to find the average number of miles he should bike on his remaining 4 bike rides this week.
Sorry for the inconvenience, but I need this done and I need help. This is the last question of this quiz. Please Help.
Answers
Answer: Ed should bike at least more than 16 miles
Step-by-step explanation:
11 + 4b > 75
4b > 64
b > 16
ommon Unit Assessment (MC) I 4 of 12
Christopher determines the system of s(x) and (x) has only one solution. Which system is Christopher solving?
A
X +3
s(x) =
X-5
+1 and t(x) = x +3 +2
ОВ.
s(x) = x2
and t(x) = In(x +7)+4
C. s(x) = 2x42 -5 and t(x) = -x +31+2
OD. $(x) = (x +3 -1 and t(x) = 2x - 5
Answers
Answer:
D
Step-by-step explanation:
I had the same question and I got this right
Christopher is solving a system of equations that has one solution and can be seen in Option C.
What is a system of equations?A system of equations is two or more equations that can be solved together to get a unique solution. In this situation, the power of the equation must be in one degree.
A quadratic equation is the second-order degree algebraic expression in a variable.
s(x) = 2x42 -5 and t(x) = -x +31+2
However, if their power is not in one degree, the quadratic equation produces two solutions.
From the given options, we can see that only option c is not a quadratic equation, Hence, it is the right answer.
Learn more about systems of equations here;
brainly.com/question/14323743
PLZ HELP IF CORRECT ILL GIVE U BRAINLIEST
Answers
Answer:
32.25
Step-by-step explanation:
Janet paid 5% interest on a $628 loan for 4 months. How much interest did she pay on her loan
Answers
Answer:
Total interest paid:$6.56
Step-by-step explanation:
I used multiple loan calculators.
What is
Mean
Medium
And Mode
Answers
Answer:
mean is the average value in the list.
first you add all number, then divide that value by the total number in the list
lets say (2,3,4,5)
you add 2+3+4+5 = 15 / 4
4 is the count
you'll get the average.
medium is the middle value in the list, but you should list from least to greatest
mode is repeated value in the list
Answer:
Step-by-step explanation:
The "mean" is the "average" you're used to, where you add up all the numbers and then divide by the number of numbers. The "median" is the "middle" value in the list of numbers.
The median is the value separating the higher half of a data sample, a population, or a probability distribution, from the lower half. In simple terms, it may be thought of as the "middle" value of a data set. For example, in the data set {1, 3, 3, 6, 7, 8, 9}, the median is 6, the fourth number in the sample. The median is a commonly used measure of the properties of a data set in statistics and probability theory.
The mode is the value that appears most often in a set of data. The mode of a discrete probability distribution is the value x at which its probability mass function takes its maximum value. In other words, it is the value that is most likely to be sampled.
Becky, an artist, plans to paint and sell some miniature paintings. She just bought some brushes for $1, and paint and canvas for each painting costs $21; she will sell each painting for $22. Once Becky sells a certain number of her paintings, she will be breaking even. How much will Becky have earned? How many paintings will that be?
Answers
Answer:
After one unit is sold, Becky will break-even.
Step-by-step explanation:
Giving the following information:
Fixed costs= $1
Unitary variable cost= $21
Selling price= $22
The break-even point is the number of units required to cover the fixed costs after deducting from the selling price the variable components. At this point, net income is zero.
Break-even point in units= fixed costs/ contribution margin per unit
Break-even point in units= 1 / (22 - 21)
Break-even point in units= 1
After one unit is sold, Becky will break-even.
A furniture store sell kits that customers use to build cabinets. Each kit contains 18 screws and a set number of boards. Jarred buys 6 of these kits and has a total of 192 screws and boards. The equation shown represents this situation: 6(x + 18) 192. What does the variable represent in Jarred's equation? * O The number of screws in one kit O The number of screws in all 6 kits O The number of boards in one kit? The number of boards in all 6 kits?
Answers
the number of boards in all 6 kits
✔✔
Triangle JKL is shown below.
K
24
L
28
Which equation should be used to find the
length of JK?