Answer:
(a) [tex]P(x) = 1342.7x + 64792[/tex]
(b) [tex]P(60) = 145354[/tex]
(c) [tex]P(x) = 64792 *1.0175^x[/tex]
(d) [tex]P(60) = 183491[/tex]
(e) The exponential model is more realistic
Step-by-step explanation:
Given
[tex]1990 ==> P_0 =64792[/tex]
[tex]2010 ==> P_{20} =91646[/tex]
Solving (a): The linear model of the population growth
First, we calculate the slope of the function.
[tex]m = \frac{P_{20} - P_0}{20 - 0}[/tex]
[tex]m = \frac{91646 - 64792}{20 - 0}[/tex]
[tex]m = \frac{26854}{20}[/tex]
[tex]m = 1342.7[/tex]
The linear equation is then calculated using:
[tex]P(x) - P_0 = m(x - x_0)[/tex]
[tex]P(x) - 64792 = 1342.7(x - 0)[/tex]
[tex]P(x) - 64792 = 1342.7(x)[/tex]
[tex]P(x) - 64792 = 1342.7x[/tex]
Make P(x) the subject
[tex]P(x) = 1342.7x + 64792[/tex]
Solving (b): The population in 2050
First, calculate x:
[tex]x = 2050 - 1990[/tex]
[tex]x = 60[/tex]
Substitute 60 for x in [tex]P(x) = 1342.7x + 64792[/tex]
[tex]P(60) = 1342.7 * 60 + 64792[/tex]
[tex]P(60) = 80562 + 64792[/tex]
[tex]P(60) = 145354[/tex]
The population in 2050 is 145354
Solving (c): The exponential model of the population growth
An exponential model is:
[tex]y = ab^x[/tex]
In this case, it is:
[tex]P(x) = P_0 * b^x[/tex]
For x = 20, we have:
[tex]P(20) = P_0 * b^{20[/tex]
Substitute values for P(20) and P0
[tex]91646 = 64792 * b^{20[/tex]
Divide both sides by 64792
[tex]\frac{91646 }{64792} = \frac{64792 * b^{20}}{64792}[/tex]
[tex]\frac{91646 }{64792} = b^{20}[/tex]
[tex]1.41446474873 = b^{20}[/tex]
Take the 20th root of both sides
[tex]\sqrt[20]{1.41446474873} = b[/tex]
[tex]b = \sqrt[20]{1.41446474873}[/tex]
[tex]b = 1.0175[/tex]
So, the model is:
[tex]P(x) = P_0 * b^x[/tex]
[tex]P(x) = 64792 *1.0175^x[/tex]
Solving (d): The population in 2050
First, calculate x:
[tex]x = 2050 - 1990[/tex]
[tex]x = 60[/tex]
Substitute 60 for x in [tex]P(x) = 64792 *1.0175^x[/tex]
[tex]P(60) = 64792 *1.0175^{60[/tex]
[tex]P(60) = 64792 *2.832[/tex]
[tex]P(60) = 183490.944[/tex]
[tex]P(60) = 183491[/tex] ---- approximated
(e) The most realistic model
The exponential model is more realistic. This is so because:
The linear model grows at a constant linear rate which means that, every year a certain amount of individuals is added to the society. However, this is not always so because it is almost impossible to for growth rate to be constant
A curve in the exponential model shows that the addition of individuals in the society every year is not always constant.
Which polynomial function has a leading coefficient of 1, roots -2 and 7 with multiplicity 1, and root 5 with multiplicity 2?
Answer:
(D)
Step-by-step explanation:
If it has a leading coefficient of 1, then it can not (A) or (B) because they have a two in front of it. Next, we can check the roots -2 and 7. -2 goes with (x+2), while 7 goes with (x-7). Therefore, you can already see that the answer is (D). To make sure. let us check the root 5 with multiplicity of 2. 5 goes with (x-5), implying that there must be 2 (x-5)'s. Only (D) satifies that as well, so the answer must be (D).
Answer:
D on edge
Step-by-step explanation:
The graph shows your elevation during a run. Which statement is true about your run?
A- You were running uphill for the first 15 minutes.
B- You were running uphill between 10 and 20 minutes into the run.
C- You were running downhill for the last 10 minutea.
D- You were running downhill the first 15 minutes.
Answer:
Its D. You were running downhill the first 15 minutes.
Mr. Hartman, the school librarian, is ordering new keyboards and mice for all of the school's computer labs. Each keyboard costs $13.50, and each mouse costs $6.50. There are 3 computer labs in the school, and each computer lab has s computer stations. Pick all the expressions that represent how much Mr. Hartman will spend on new keyboards and mice.
Answer:
3 * 20s
Step-by-step explanation:
In order to find out how much Mr. Hartman will spend in total we first need to multiply the price of the keyboard and mouse by the number of computers in a single computer station. Once we have these products we add them together. Finally, we multiply this new value by 3 since there are a total of 3 computer stations. If we turn this into an expression it would be the following...
3 * (13.50s + 6.50s)
We can even simplify this by first adding the cost of the keyboard and mouse and then multiplying by s
3 * 20s
pls answer this question
Answer:
id kkk what the quequestion is
Step-by-step explanation:
write the fraction in ascending order.
from most to least:
i: 1/2, 1/3, 1/7, 1/10
ii: 2/3, 2/5, 2/9, 2/11
iii: 5/6, 3/4, 2/3, 1/2
iv: 4/5, 3/4, 5/8, 1/2
P = 100 - 20 cos (8πt/3) That's (8 pi t /3) where t is the time (in seconds). What is the period of the model? Discuss what the period represents in the context of this model.
Answer:
The period of the model is [tex]\frac{3\pi}{4}[/tex] seconds. The period represents the time needed for the function to complete one cycle.
Step-by-step explanation:
Cosine is a trigonometric function and trigonometric functions are characterized by having a periodical behavior. The period is the time needed for the function to cover an angle of [tex]2\pi[/tex] radians. By this approach we find that:
[tex]\frac{8\pi\cdot t}{3} = \frac{2\pi\cdot t}{T}[/tex] (1)
Where:
[tex]t[/tex] - Time, measured in seconds.
[tex]T[/tex] - Period, measured in seconds.
Then, we solve (1) for [tex]T[/tex]:
[tex]\frac{8}{3} = \frac{2\pi}{T}[/tex]
[tex]T = \frac{6\pi}{8}\,s[/tex]
[tex]T = \frac{3\pi}{4}\,s[/tex]
The period of the model is [tex]\frac{3\pi}{4}[/tex] seconds. The period represents the time needed for the function to complete one cycle.
Dado los puntos p1 (-7/2-9/2) y p2 (5/2, 3/2) calcular la representación gráfica, d p1 p2, pto medio de p1 p2, la pendiente (m) de la recta que pasa por medio de ellos. Porfavor ayúdenme la tarea es para el viernes y no entendió
Answer:
Ce clasă ești sa văd daca te pot ajuta
Solve the equation f/ 1.4 = 6
Step-by-step explanation:
[tex] \frac{f}{1.4} = 6 \\ [/tex]
[tex]f = 6 \times 1.4[/tex]
[tex]f = 8.4[/tex]
Answer:
The answer to your question is 8.4
plz help asap!!
which statement is not true about the data shown by the box plot below ?
Answer:
B
Step-by-step explanation:
the range is about 45
The Value of (441)2 – (440)2 is :
(i) 841 (ii) 1 (iii) 881 (iv) 0
Find the slope of the line y= -8/5x + 2
Step-by-step explanation:
Given
y = - 8 /5 x + 2
Comparing the given equation with y = mx + c
slope (m) = - 8/5
Hope it will help :)
Answer:
-8/5
Explanation:
The equation is written in slope-intercept form, aka y = mx + b, where m is the slope and b is the y-intercept.
In slope intercept, the slope is always the number that comes before x.
In the equation y = -8/5x + 2, that number is -8/5.
Hence, the answer is -8/5.
Despite a wide variety of workplaces for those working in Human Services, all workplaces include
comfortable areas for interactions amongst people.
a variety of medical testing equipment.
desks where clients can sit across from the worker.
toys and exercise equipment for children.
Answer:
a variety of medical testing equipment.
Step-by-step explanation:
Answer:
c hope this helps if wrong please tell me
Step-by-step explanation:
Can someone help me with this problem? 3[x(-6)]
Answer:
-18x
Step-by-step explanation:
First step: remove the parentheses.
So, you'll have -3x*6.
multiply the numbers (3 x 6 = 18)
and you'll get -18x.
hope this helps!
Is 7/8 equivalent to -7/-8
Answer:
No
Step-by-step explanation:
I don't think those are equivalent because 7/8 is positive while -7/-8 is negative.
Tyrone has 16 model airplanes on his shelf. He has 4 times as many model airplanes as model trains. How many model trains does Tyrone have?
Write multiplication and division equations to model and solve the problem. Use m for the unknown
Answer:
Step-by-step explanation:
m=16/4 this one is division
16= 4*m multiplacation
Answer the photo below thanks
Answer:
6x60=360
Step-by-step explanation:
60
Solve and graph the inequality.
7n - 1 > 76
Answer:
n>11
Step-by-step explanation:
I don't know how to graph this answer, sorry!
The solution of the inequality 7n - 1 > 76 gives n < 11 along with the graph.
Given Inequality:
7n - 1 > 76
To solve the inequality add 1 on both side of inequality as
7n - 1 + 1 > 76 + 1
7n > 77
Now, divide the inequality by 7 as
7n/ 7 > 77/ 7
n > 11.
Therefore, the solution is n > 11.
Learn more about Inequality here:
https://brainly.com/question/28823603
#SPJ6
Each week, the price of oranges at the farmer's market increases by 20%. The price of oranges this week is 2.50 What was the price last week
Answer:4.50
Step-by-step explanation:
Algebraic Expression
x + y + 2
Constants | Variable/s/term/s Degree of term
Constants : 1 (the only constant term is 2)
Variables : 2 (x and y)
Terms : 3 ( x, y and 2)
Degree of term : 1
What is s??
A 44°
B 35.3°
C. 37.9°
D. 22°
Answer: Choice B) 35.3 degrees
======================================================
Work Shown:
Apply the law of sines
sin(S)/s = sin(R)/r
sin(S)/16 = sin(120)/24
sin(S) = 16*sin(120)/24
sin(S) = 0.57735026918962
S = arcsin(0.57735026918962)
S = 35.2643896827542
S = 35.3
Make sure your calculator is in degree mode.
45 is 3% of what number?
quick I need an answer!
hurry pls!
Answer:
stop rushing brat
Step-by-step explanation:
Step-by-step explanation:
Steps to solve "45 is 3 percent of what number?"
We have, 3% × x = 45
or,
3
100
× x = 45
Multiplying both sides by 100 and dividing both sides by 3,
we have x = 45 ×
100
3
x = 1500
If you are using a calculator, simply enter 45×100÷3, which will give you the answer.
11. Select from below the best estimate for the decimal that is equivalent to 100.5%
A. 0
B. 1
C. 100
D. 1000
Answer:
c
Step-by-step explanation:
in all honesty because if you round thats what you would get
a rectangular garden measures 22.7 m by 16.6 m how many meters of fencing materials are needed to enclose it the fencing materials cost 12.50 per meter
Answer:
78.6m of fencing
That would cost $982.50
Step-by-step explanation:
Perimeter: 2(22.7)+2(16.6)=P
P = 78.6
Cost: 78.6*12.50
C = 982.50
The weights of four puppies are shown in pounds
9.5 9
9.125 9
Which list shows these weights in order from greatest to least?
Answer:
9.125 9, 9.59
Step-by-step explanation:
please help and show work
To prove that the triangle is scalene, calculate all the lengths of the sides.
The formula for a line like this is basically pythagorean theorem, which is
[tex]p = \sqrt{ {(y2 - y1)}^{2} + {( x2 - x1})^{2} } [/tex]
(x1, y1) and (x2, y2) are the respective vertexes.
Dora buys some T-shirts for $8.75 each and pairs of shoes for $27.50 each. If she buys 4 T-shirts, how much money would she have to spend in all
8.75*4=35 so $35 for shirts
and depending on how many shoes she buys but lets just say one pair
35+27.50= 62.50 so it would be a total of $62.50
Step-by-step explanation:
4 shirts with each price $8.75 = 4 × $ 8.75= $ 351 pair of shoes with price = $ 27.50so total price = $ 35 + $ 27.50 = $ 62.50MARK ME AS BRAINLISTPLZ FOLLOW MEI need the answer, ASAP.
Answer:
See below.
Step-by-step explanation:
It is similar because the order of operations is the same for fractions and for whole numbers.
It is different because when you add or subtract fractions, you need a common denominator. When you deal with whole numbers, there are no denominators.
If the blue radius below is perpendicular to the chord , which is 14 units long, what is the length of the segment ?
Answer:
The answer is 7 bc 7 is half of 14
Step-by-step explanation:
I’ll give brainlist to anyone that can help me
Answer:
80 ft
Step-by-step explanation:
if 1 = 20 then 20 is width but ? is length
1=20
2=40
3=60
4=80
since 4 in is length then actual length is 80ft
Answer:
80ft
Step-by-step explanation:
hope this helps
-8-8(6x+1) i can’t solve this
Answer:
Step-by-step explanation:
Answer: -48x-16
Step-by-step explanation:
-8-8(6x+1)
So we are going to let the first -8 stand still for a moment and focus on the "-8(6x+1) part. We will solve this using distributive property.
-8 x 6x = -48x
and
-8 x 1 = -8
This is our new problem -8 -48x -8 .
Lets do like terms. Our like terms are (-8) and (-8). And we know -8 -8 = -16.
Now we'll add that to our (-48x) . I hope you can understand this!