Given:
Consider the given function is:
[tex]P(t)=4000(1.2)^t[/tex]
To find:
a. The type of exponential function (growth or decay).
b. Percentage change in population.
c. Population after 5 years.
Solution:
a. The general exponential function is:
[tex]P(t)=P_0(1+r)^t[/tex] ...(i)
Where, [tex]P_0[/tex] is the initial population and r is the rate of change in decimal.
If r<0, then the function represents exponential decay and if r>0, then the function represents exponential growth.
We have,
[tex]P(t)=4000(1.2)^t[/tex]
It can be written as:
[tex]P(t)=4000(1+0.2)^t[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]P_0=4000[/tex]
[tex]r=0.2[/tex]
Since r>0, therefore the given function represents exponential growth.
b. From part (a), we have
[tex]r=0.2[/tex]
So, the rate of change in the population is 0.2. Multiply is by 100 to get the percentage change in population.
[tex]r\%=0.2\times 100[/tex]
[tex]r\%=20\%[/tex]
Therefore, the yearly percentage change in population is 20%.
c. We have,
[tex]P(t)=4000(1.2)^t[/tex]
Substitute [tex]t=5[/tex] in the given function to find the population living on the island after 5 years.
[tex]P(5)=4000(1.2)^5[/tex]
[tex]P(5)=4000(2.48832)[/tex]
[tex]P(5)=9953.28[/tex]
[tex]P(5)\approx 9953[/tex]
Therefore, the estimated population living on the island after 5 years is 9953.
Figure ABCD was reflected across the x-axis to create figure A'B'C'D'.
On a coordinate plane, a quadrilateral has points A prime (2, negative 2), B prime (negative 8, 2), C prime (2, 6), and D prime (8, 2).
What are the coordinates of the pre-image of B'?
(2, –8)
(–8, –2)
(–2, 8)
(8, 2)
Answer:
(-8 , -2)
Step-by-step explanation:
the coordinates of B’ are (-8 , 2)
then
Since B also is the image of B’ through the reflection across the x-axis
then the coordinates of B are (-8 , -2)
Answer:
(-8, -2)
Step-by-step explanation:
How do I solve 3x+7+x?
Answer:
The answer is 4x+7
Step-by-step explanation:
3x+7+x
= 3x+x+7
= 4x+7
(I used symbolab)
-64+k^2=0 solve this using quadratic formula
Answer:
x= +8 or -8
Step-by-step explanation:
x= -b±[tex]\sqrt{b^2-4ac}[/tex] /2a
x=−0±[tex]\sqrt{0^2 negative4(1)( negative 64)}[/tex] /√2(1)
x=−0±0[tex]\sqrt{256}[/tex]/√2
x=−0±256−−−√2
x=−0±162
x=16/2 x=−16/2
x=8
x=−8
On a map, 1/4 inch represents 400 miles. How long would a line on a map need in order to represent 3200 miles?
Answer:
2 inches
Step-by-step explanation:
1/4 = 400
3200/400 = 8
8 x 1/4 = 2
A line on a map need in order to represent 3200 miles would be 2 inches long.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
On a map, 1/4 inch represents 400 miles.
1/4 = 400
3200/400 = 8
8 x 1/4 = 2
A line on a map need in order to represent 3200 miles would be 2 inches long.
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Hi there. May you please help if you can!
A(-4, 1), B(1, 5), C(4, -3), and D(-2, -3) are the vertices of a quadrilateral. Determine the coordinates of the image vertices after each transformation of ABCD. a) a reflection in the x-axis b) a reflection in the y-axis c) a rotation of 180° cw about the origin d) a rotation of 270° cw about the origin
Show your work
Answer:
hello brother or sister can you please send a picture of the graph in provided but if not there are no specific calculations on reflection so you have to be smart on it and try imagining it or have your own scratch
Jaideep changes $12 000 into euros (€) to buy land in another country.
The exchange rate is €1 = $1.33.
Calculate the number of euros Jaideep receives.
A farmer sold food grains for 9200 rupees through an agent. The rate of commission
was 2%. How much amount did the agent get?
The price of a machine depreciates at 10% every year. If the present value of the
machine be Rs.100000, what will be its value after 3 years?
Lucinda invests $500 at a rate of 5% per year simple interest.
Calculate the simple interest Lucinda has after 3 years.
PLEASE GIVE ANSWERS TO THESE QUESTIONS REALLY QUICK
exercise 1
1) 12 000 : 1,33 = 9022,55 €
exercise 2
1) 9200 : x = 100% : 2%
(9200*2) : 100 = 184 rupees
(sorry dont know the other two ones)
One half of the number n increased by 10 is the
same as four less than twice the number.
Which of the following equations represents the
statement above?
Answer:
Step-by-step explanation:
[tex]\frac{n}{2} +10=2n-4[/tex]
The equation represent the given situation is n/2 -10 =2n-4.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
Given that, One half of the number n increased by 10.
That is n/2 -10
Four less than twice the number.
Here, 2n-4
Now, n/2 -10 =2n-4
n/2 -2n = -4+10
(n-4n)/2 = 6
-3n=12
n=-4
Therefore, the equation represent the given situation is n/2 -10 =2n-4.
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The directrix of the parabola -40x= y2 is:
y=-10
x= 10
x=-10
y= 10
Answer:
y=10
Step-by-step explanation:
Answer:
[tex]{ \tt{y {}^{2} = 4 {ax} }} \\ = - 10[/tex]
Helpppppp!!’nnnnnnn.
Answer:
35.75
Step-by-step explanation:
times 65 by 55%
A pole 11 feet tall is used to support a guy wire for a tower, which runs from the tower to a metal stake in the ground. After placing the pole, Jayden measures the distance from the pole to the stake and from the pole to the tower, as shown in the diagram below. Find the length of the guy wire, to the nearest foot. 11 ft 20 ft-8 ft
Answer:
48 ft
Step-by-step explanation:
Here, we want to find the length of the wire
from the diagram, we can identify two similar triangles
The smaller one and a bigger one
Mathematically, when two triangles are similar, the ratio of their corresponding sides are equal
We can start by getting the height of the tower
we have this as:
8/11 = 28/x
8 * x = 28 * 11
8x = 308
x = 308/8
x = 38.5 ft
So as we can see, the wire represents the hypotenuse of the larger triangle that measures 28 ft base and 38.5 ft height
So we can use the Pythagoras’ theorem to get the hypotenuse
Let us call this g
mathematically according to the theorem, the square of the hypotenuse equals the sum of the squares of the two other sides
thus, we have it that;
g^2 = 38.5^2 + 28^2
g^2 = 2,266.25
g = √2,266.25
g = 47.61 which is approximately 48 ft
Solution
We know the angles here are vertical angles and we know that vertical angles are always congruent
Answer:
4 + 6x = 70
6x = 66
x = 11
Help,anyone can help me do quetion,I will mark brainlest.
Answer:
Step-by-step explanation:
B3)
z + 127 = 180 {linear pair}
z = 180 - 127
z = 53
y= 55 {Corresponding angles}
w + z + y = 180 {angle sum property of triangle}
w + 53 + 55 = 180
w + 108 = 180
w = 180 -108
w = 72
x = w {Vertiaclly opposite angles}
x = 72
B4) q + 101 = 180 {Linear pair}
q = 180 -101
q = 79
p = 142 {Corresponding angles}
p + s = 180 {linear pair}
142 + s = 180
s = 180 - 142
s = 38
s +q +r = 180 {angle sum property of triangle}
38 + 79 + r = 180
117 + r = 180
r = 180 - 117
r = 63
y + 63 = 180 {linear pair}
y = 180 - 63
y = 117
x = q = {corresponding angles}
x = 79
If chicken wire comes in rolls that are 48 inches long, determine the smallest amount of rolls that will be needed to fence the garden
Answer:
No solution is possible from the information provided.
Step-by-step explanation:
if def geh solve for x
Answer:
huh???
Step-by-step explanation:
Find the length of the arc. Leave the answer in terms of π
Jamar has a points card for a movie theater. He receives 20 rewards points just for signing up. He earns 12.5 points for each visit to the movie theater. He needs at least 95 points for a free movie ticket.
Find the mean of the data set:
10, 8, 7, 7, 9, 10
Answer:
jk
Step-by-step explanation:
Answer:
nxgxhdhdjdkdkdjdjjddbdvd f fvfbfbfnfjjfcjjfjfjfjfjdjdjdjdjdjdjdjdjdjjjdjdjfjfjfjfjffjfjfjfjfjf
Somebody plz help the quickest you can this is urgent
Answer:
Well, I can answer the 1st question. There are 2 angles and 3 sides on the triangle.
Step-by-step explanation:
A bag of white sugar and a bag of brown sugar each contain 11 1/3 cups of sugar. How Many muffins can Maria top if she has 1 bag of each type of sugar?Explain your reasoning。This is super urgent tahnks
Answer:
187
Step-by-step explanation:
Fraction to make topping:
1/4 cups of white ; 2/3 cups of brown
Combined = 1/4 + 2/3 = (3 + 8) /12 = 11/12 cups
Fraction of combined used to top muffin = 1/12
Number of muffins that can be topped per combination made :
11/12 ÷ 1/12 ; 11 /12 * 12 / 1 = 11 muffins
Recall :
Each sugar has 11 1/3 cups
For brown sugar :
34 /3 ÷ 2/3 cups
34 /3 * 3 /2 = 17
For white sugar :
34 /3 * 4 /1 = 45.33
However, the highest amount of combined muffin topping for white sugar will be restricted by the number of brown :
Hence,
11 muffins can be topped from each combined mixture ;
Total muffin that can be topped :
17 * 11 = 187 muffins
Using the triangle diagram below in the rules for special right triangles, discover the four missing links and choose them from the available choices:
Answer:
The solution for the system of right triangles are, respectively: [tex]a = 2\sqrt{6}[/tex], [tex]b = 4\sqrt{3}[/tex], [tex]c = 4\sqrt{6}[/tex], [tex]d = 6\sqrt{2}[/tex]
Step-by-step explanation:
By Geometry, we get the following equivalencies:
[tex]a = 2\sqrt{6}[/tex] (45 - 45 - 90 Theorem)
[tex]b = \sqrt{2}\cdot (2\sqrt{6})[/tex] (45 - 45 - 90 Theorem)
[tex]b = 4\sqrt{3}[/tex]
[tex]c = \frac{2\sqrt{6}}{\frac{1}{2} }[/tex] (30 - 60 - 90 Theorem)
[tex]c = 4\sqrt{6}[/tex]
[tex]d = \frac{2\sqrt{6}}{\frac{\sqrt{3}}{3} }[/tex] (30 - 60 - 90 Theorem)
[tex]d = 6\sqrt{2}[/tex]
According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function? (9x + 7)(4x + 1)(3x + 4) = 0 1 root 3 roots 4 roots 9 roots
Answer:
Step-by-step explanation:
3 roots
namely -7/9,-1/4.-4/3
Solve. -3 + 9x = 24 pls help 15 pts!!! ASAP
Answer:
hope it is helpful to you
Which ordered pair is the best approximation of the solution?
Answer:
D. (0.6, 1.3)
Step-by-step explanation:
we see in the table that the smaller x the smaller the difference between the y values of both functions. but it must not get too small, as for x=0.5 the difference gets bigger again.
the minimum difference we see for x=0.6. and the y-values are 1.2 and 1.4.
the solution of the system of equation means that both y values are the same for the "shared" x-value (which is the solution of the system, the point where both functions cross each other).
so, we consider 0.6 the best approximation for the true solution for x. and the solution for y is then somewhere in the middle between 1.2 and 1.4. so, 1.3 is a good approximation.
therefore, (0.6, 1.3) is the closest (= best) approximation to the real solution of all provided answer options.
Just B please. It’s not 4:3 tho please can someone helo
Answer:
The workout ratio of the online sales to shop sales is 1:3
Step-by-step explanation:
Given:
A jewelry shop sells 240 necklaces in a month. 180 of the necklaces were sold via the shops website. The rest were sold in a High Street shop.
To find:
Work out the ratio of online sales to shop sales.
Solution:
Total no necklaces = 240
Necklace sold on website = 180
Remaining necklace sold via street = 240 - 180 = 60
Ratio = 60 : 180 = 1 : 3
a rectangular solid box measures 2.17 feet by 4.05 feet by 480 inches. in cubic yards, what is the volume of the box? express your answer as a decimal to the nearest tenth
Answer:
117.18 yards
Step-by-step explanation:
480in=40ft
2.17x4.05x40=351.54tf
351.54ft=117.18yrds
A. The vertical scale is too high.
B. The vertical scale should not start at zero.
C. The bars are not the same width.
D. The bars are not the same height.
A rectangular prism tank has a base with a length of 40 inches, a width of 35 inches and a height of 12 inches. What is the volume of water in the tank if the tank is filled with water to 75% capacity ?
Answer:
12600 in³
Step-by-step explanation:
Applying,
V = lwh................. Equation 1
Where V = volume of the prism, l = length of the base, w = width of the base, h = height of the prism.
From the question,
Given: l = 40 inches, w = 35 inches, h = 12 inches
Substitute these values into equation 2
V = 40(35)(12)
V = 16800 in³
If the volume of water is 75% the capacity of tank.
Therefore,
Volume of water = 0.75(V)
Volume of water = 0.75(16800)
Volume of water = 12600 in³
What is the value of the expression. -(2 1/2 - 7) - 6 1/2?
Answer:-2
Step-by-step explanation:
If line segment are you is considered the base of a parallelogram are STU what is the corresponding height of the parallelogram
Answer: Hello your question lacks some data hence i will provide a general solution within the scope of your question.
answer:
Height = Area of parallelogram / base of parallelogram
Step-by-step explanation:
The corresponding height of the parallelogram can be calculated using the general equation below :
Height = Area of parallelogram / base of parallelogram
Kindly input the values you have into the relation to get the corresponding height of the parallelogram.
Brainliest goes to whoever answers correctly and explains also if you want extra points answer my other questions
Answer:
Step-by-step explanation:
The y intercept, also known as 'c' in the formula y = mx + c acts as the coordinate for y when x = 0 [E.g. (0, 24) which c = 24]
Question 1 = y = -5x + 50
On the graph, c = 50 [ y = mx + 50 ]
30 - 15 = 15
7 - 4 = 3
15/3 = 5 (for the gradient, or 'm', which you may use the formula 'rise/run' on the line shown) [ y = 5x + 50 ]
ALTHOUGH, in question one, the line has a Negative Correlation, it slants downwards on the slope, so the gradient will be negative : y = -5x + 50
If x = 9, y = (9 x -5) + 50, = -5
y = -5
Question 2 = y = 2.5x + 5
c = 5
m = 5/2 = 2.5
y = 2.5x + 5
when y = 30 > x = 10
30 = 2.5x + 5
30 - 5 = 25
25 = 2.5x
x = 25/2.5
x = 10
Question 3 = y = -10x + 50
c = 50
m = (30 - 20) / 1 = 10
y = -10x + 50
when x = 4 > y = (-10 x 4) + 50
y = -40 + 50
y = 10