Answer:
Approximate population ≈ 74.36 million.
Step-by-step explanation:
The given problem involves modeling of an exponential growth or decay function of a population.
Definition:Exponential growth ( relative growth ) occurs when a population grows or increases exponentially by the same factor, over the same amount of time. Exponential decay occurs when a population decreases continuously by a constant factor, over the same amount of time.We can model the exponential growth of a population using the following Exponential Growth Model:
⇒ [tex]\displaystyle\mathsf{P(t)\:=\:P_0 (1\:+\:r)^t }[/tex]Where:
P( t ) = population after "t" years P₀ = initial population r = relative growth rate; positive "r" value means that the population is increasing; negative "r" value implies that the population is decreasing. t = time (typically in years)Solution:Based from the given equation, [tex]\displaystyle\mathsf{y\:=\:58.7(1.03)^t }[/tex] , we can infer that:
⇒ [tex]\displaystyle\mathsf{P(t)\:=\:P_0 (1\:+\:r)^t }[/tex] or [tex]\displaystyle\mathsf{y\:=\:P_0 (1\:+\:r)^t }[/tex]
Where:
P( t ) or y = population after "t" yearsP₀ = initial population = 58.7r = relative growth rate = 0.03 or 3% = the population is increasing (exponential growth).t = time (typically in years) = 8 years (difference between January 2002 and January 1994).Step 1: Substitute the given values into the Exponential Growth Model formula, and solve for P( t ) :
[tex]\displaystyle\mathsf{P(t)\:=\:P_0 (1\:+\:r)^t }[/tex]
⇒ [tex]\displaystyle\mathsf{P(8)\:=\:58.7 (1\:+\:.03)^8 }[/tex]
Step 2: Follow the order of operations, addition inside the parenthesis:
⇒ [tex]\displaystyle\mathsf{P(8)\:=\:58.7 (1.03)^8 }[/tex]
Step 3: Follow the order of operations, applying the exponent into the parenthesis (do not round off the digits inside the parenthesis):
⇒ [tex]\displaystyle\mathsf{P(8)\:=\:58.7 (1.266770081) }[/tex]
Step 4: Follow the order of operations, multiplying 58.7 (P₀) into the parenthesis:
⇒ [tex]\displaystyle\mathsf{P(8)\:\approx \:74.35940378\quad or \quad 74.36\:\:million}[/tex]
Final Answer:Therefore, the approximate population of the country in January 2002 is 74.36 million.
________________________Keywords:Exponential functions
Exponential growth
Exponential decay
Exponential growth model
____________________________
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Find the area of the figure.
Answer:
132cm2
Step-by-step explanation:
1. Split the figure into a trapezoid and a rectangle.
2. Find the area of the trapezoid, which is 104cm2.
3. Find the area of the rectangle, which is 28cm2.
4. Add the areas to get 132cm2.
Madeline uses this scale model of a design she plans to paint on a wall. She uses the key 1 cm = 1. 5 ft. One gallon of paint will cover 400 square feet of wall. How many gallons of paint will Madeline use? Enter your answer as decimal in the box.
The amount of paint required by Madeline will be 0.8325 gallons
What amount of paint will be required by Madeline?Given that
[tex]1cm=1.5ft[/tex]
We will first find the area of the wall
Area of the wall = Area of trapezoidal shape+ Area of triangular shape
Area of trapezoid = [tex]\dfrac{a+b}{2} \times h[/tex]
a= 4cm
b=14cm
h=10cm
putting this values
[tex]A=\dfrac{4+14}{2} \times 10[/tex]
[tex]A=90cm^{2}[/tex]
Area of triangular shape= [tex]\dfrac{1}{2} \times width\times height[/tex]
width=14cm
height=8cm
putting the values
[tex]A=\dfrac{1}{2} \times 14\times 8=58cm^{2}[/tex]
[tex]Total area of the wall= 90+58=148cm^{2}[/tex]
since we have
[tex]1cm=1.5ft[/tex]
[tex]148cm^{2} = 148\times (1.5)^{2} =333 ft^{2}[/tex]
Now
[tex]1gallon = 400ft^{2}[/tex]
so for [tex]333 ft^{2}[/tex] amount of paint in gallons required will be
[tex]1ft^{2} =\dfrac{1}{400} gallons[/tex]
[tex]333ft^{2} =\dfrac{333}{400} gallons=0.8325gallons[/tex]
Thus the amount of paint required by Madeline will be 0.8325 gallons
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Rewrite the following equation in slope intercept form. 7x - 20y = -11
Answer:
y=7/20x+11/20
Step-by-step explanation:
7x-20y=-11
20y=7x-(-11)
20y=7x+11
y=7/20x+11/20
Can the sides of a triangle have lengths 3.4, 11.6, and 12.6?
I NEED HELP!
Find the volume.
Thanks!
Answer:
364
Step-by-step explanation:
Hello, you can use the formula which is [tex]v=lwh/3[/tex]
if CE=5, YF=21 and XZ=15, determine and state the perimeter of triangle CFX.
The perimeter of the triangle CFX is the sum of lengths CF, FX and XC
The perimeter of the triangle CFX is 82 units
How to determine the perimeter of triangle CFXThe given parameters are:
CE=5, YF=21 and XZ=15
Points E, Y and Z are the median of the triangle CFX.
This means that:
CF = 2 * CE
FX = 2 * YF
XC = 2 * XZ
The perimeter of triangle CFX is then calculated as:
Perimeter = CF + FX + XC
This gives
Perimeter = 2 * CE + 2 * YF + 2 * XZ
So, we have:
Perimeter = 2 * 5 + 2 * 21 + 2 * 15
Perimeter = 82
Hence, the perimeter of the triangle CFX is 82 units
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What is a corner of a kitchen counter?
Answer:
vertices
Step-by-step explanation:
The corner of a shape or object is the vertices
An office supply company is shipping a case of
wooden pencils to a store. There are 64 boxes of
pencils in the case. If each box of pencils weighs
2.5 ounces, what is the weight, in pounds, of the
case of wooden pencils?
Select all equations that are equivalent to 8 + 3x = -2(11)
a. 8 + 3x 2(11)
b. 8+3x/2 = -11
c. -8 -3x = 2(11)
d. 2(8+3x) = -4(11)
e. 11x = -22
Answer:
HERE
Step-by-step explanation:
All equations equivalent to 8+3x = -2(11) are:
2(8+3x) = -4(11) and -8 - 3x = 2(11)
please mark brainliest!What is the 83rd term of the arithmetic sequence an=9,11,13,15,17,19
Answer:
173
Step-by-step explanation:
substitute and calculate
This composite figure is made up of three simpler shapes. What is the approximate area of the figure? Use 3.14 for pi.
A. 33.56 square inches
B. 33.28 square inches
C. 27.28 square inches
D. 39.56 square inches
Check the picture below.
[tex]\stackrel{\textit{\Large Areas}}{\stackrel{rectangle}{(5)(3)}~~ + ~~\stackrel{triangle}{\cfrac{1}{2}(4)(3)}~~ + ~~\stackrel{semi-circle}{\cfrac{1}{2}\pi (2)^2}}\implies 15~~ + ~~6~~ + ~~2\pi \stackrel{using~\pi =3.14}{\implies 27.28}[/tex]
which of the following would result in the same value as -40 divided by 2? select all that apply
Answer:
C D F
Step-by-step explanation:
Taking -40/2, we know our answer must be -20.
Testing each answer choice proves this.
A= 40*1/2, which is equal to 40/2, which is 20.
B= -40*-1/2, again, equaling 20.
C= 40/-2. Since one of our terms is negative, this one is -20.
D= 40*-1/2, again, -20.
E= -1/40*2. This would equal -2/40, using fraction multiplication.
F= -40*1/2, Which is the exact same thing the original question asks.
Thus, our final answer is C, D, and F.
What is the y-intercept of the equation y=10,000(0. 97)x ?
10,000
1
0. 97
0
PLEASE HELP ASAPPPP (THIS IS QUESTION 15) ALSO CONSUMER MATH
Answer:
Step-by-step explanation:
The y intercept, is when x=0, and so it is 10000(0.97)^0 = 10000
can someone help me with this question please
Answer: I feel like it’s d..
Step-by-step explanation:
Solve the simultaneous equations
2x-3y = 4
4x - y = 13
3 marks
Answer:
X=7/2 Y=1
Step-by-step explanation:
4X-Y=13
4X-13=Y
2X-3(4X-13)=4
2X-12X+39=4
-10X+39=4
-10X=4-39
-10X=-35
X=7/2(-35/10)
Y=4(7/2)-13
Y=14-13
Y=1
The solution of the two given linear equations will be equal to X=7/2 Y=1
What is an equation?
It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
The solution of the linear equation is as follows:-
4X - Y = 13
4X - 13 = Y
2X - 3 ( 4X - 13 ) = 4
2X - 12X + 39 = 4
-10X + 39 = 4
-10X = 4 - 39
-10X = -35
X = 7/2 ( -35 / 10 )
Y = 4 ( 7/2 ) - 13
Y = 14 - 13
Y = 1
Therefore the solution of the two given linear equations will be equal to X=7/2 Y=1
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What is the GCF of 16s3t, 40s5, and 68t2?
4
4s3t
8
8s3t
Answer:
4
Step-by-step explanation:
100 POINTS FOR CORRECT ANSWERS
Answer:
1. Polynomial
2. Not a polynomial
3. Not a polynomial
4. Not a polynomial
5. Not a polynomial
6. Not a polynomial
Step-by-step explanation:
Answer:
the first three are polynomials; the remainder are not
Step-by-step explanation:
A polynomial is a sum of terms with non-negative integer powers of the variables.
The first three expressions are all polynomials; the last three are not.
__
The rational expression with a variable in the denominator is a "rational function", but is not a polynomial. The expressions containing |x| and √x are not expressions that have x to an integral power.
The coefficients of the polynomials we generally deal with are usually integers or fractions. However, there is no requirement that they be rational or real. The second expression is still a polynomial even though it has irrational coefficients.
10. Given the kite at the right, DF=7 inches and Area=42 inches square.
What is the length of EG?
A. 7 in
B. 12 in
C. 14 in
D. 16 in
Leon evaluated the expression
Negative one-half(–4a – 6) + a2 for a = 8.
Answer:
[tex]26[/tex]
Step-by-step explanation:
[tex](-4a - 6) + a2[/tex]
[tex]a=8[/tex]
Let's Substitute a with 8:
[tex]-4\times \:8-6+8^2[/tex]
[tex]26[/tex]
2. You need to use 2/3 of a can of pizza sauce to make a pizza. The
can contains 1 lb 2 OZ of sauce. How many ounces do you need
for the pizza?
I really need this now I’ll give a bunch of points
Answer:
Step-by-step explanation:
The can contains 1 pound + 2 oz
1 pound = 16 oz
1 can = 16oz + 2oz
1 can = 18 oz
2/3 can = 18 oz * 2/3
2/3 can = 18 oz/1 * 2/3
Multiply the numerator * numerator divide by (denominator * denominator)
2/3 can = 36 / 3
2/3 can = 12 oz.
You could do this by cancelation, but you may not know that yet.
hi pls help will mark as brainlist
Answer:
(5x + 3x) (x -5)
Step-by-step explanation:
Factor a GCF from the expression, if possible.
Factor a Trinomial, if possible.
Factor a Difference Between Two Squares as many times as possible.
If the equation is in the form a2-b2, factor it to (a+b)(a-b). Equations with two variables factor differently than basic quadratics. For any equation a2-b2 where a and b do not equal 0, the equation factors to (a+b)(a-b). For example, the equation 9x2 - 4y2 = (3x + 2y)(3x - 2y).
What would be the correct notation for the following line
Answer:
Its A :))
Step-by-step explanation:
Solve the equation by completing the square.
X^2 – 12x = 13
First we add (-12/2)^2 to both sides to get
x^2 - 12x + 36 = 49.
Then square root each side and solve.
A. {46, 55}
B. {-15, 27}
C. {-1, 13}
D. {-21, 33}
Answer:
C
Step-by-step explanation:
x² - 12x + 36 = 49
(x - 6)² = 49
now taking the square root
x - 6 = 7
x = 13
the second solution is (remember, sqrt(a²) = ±a)
-(x - 6) = 7
-x + 6 = 7
-x = 1
x = -1
really need help on this
Answer:
9
Step-by-step explanation:
[tex] \sqrt{3 {}^{4} } =( 3 {}^{4} ) {}^{ \frac{1}{2} } = {3}^{2} = 9[/tex]
The graph represents the cost of renting a generator from a hardware store. What does the point (2, 50) mean in the problem situation?
The point (2,50) means that the Cost of renting a generator for 2 hours is $50..
The y-axis is representing the Total cost The x-axis is repressing the Time in hours9 is 3 less than a number n in standard form
Answer:
9=n-3
Step-by-step explanation:
Please help with this question
sort the sequences according to whether they are arithmetic, geometric, or neither.
Step-by-step explanation:
I am not sure what you mean by "sort". that would mean to bring them into a certain sequence.
I think you mean "categorize".
the first one is arithmetic.
the added constant is -4.2
98.3 - 4.2 = 94.1
94.1 - 4.2 = 89.9
...
the second one is neither.
it looks like first to be arithmetic with the added constant of -1.
1 - 1 = 0
0 - 1 = -1
but then
-1 - 1 = -2 and not 0.
the third is geometric.
the ratio or multiplication factor is 2.
1.75 × 2 = 3.5
3.5 × 2 = 7
...
the fourth is arithmetic.
the added constant is 1.2.
-12 + 1.2 = -10.8
-10.8 + 1.2 = -9.6
...
the fifth is geometric.
the ratio of multiplication factor is -1.
-1 × -1 = 1
1 × -1 = -1
...
if you really need to sort them (change their positions in that 5 elements list), then
the 1st and 4th are arithmetic (to be put into the top 2 spots).
the 3rd and 5th are geometric (to be put into the next 2 spots).
the 2nd is neither (last spot).
here is the question
Answer:
1) -6.4
2)71
3)15.4
what is -2y-8=-2x in slope intercept form
Answer:
y= x-4
Step-by-step explanation:
slope-intercept form is y=mx+b
-2y-8=-2x move the 8 over to the other side
-2y=-2x-8 divide whole equation by negative 2
this should give you, y=x-4