Consider the growth function f(x)=200(1.08). Describe the characteristics of the functions by using the drag and drop feature
Answers
Answer:
1) Domain: -∞ < x < +∞
2) Range: y > 0
3) y intercept: (0, 200)
4) Asymptote: y = 0
5) The growth rate; r = 0.08
6) The growth factor = 1.08
7) End Behavior: As x → -∞, f(x) → 0
8) End Behavior: As x → +∞, f(x) → +∞
Step-by-step explanation:
1) The domain of the function is given as the x values for which the function is valid which includes from -∞ < x to +∞
2) The range of the function, are the range of the output values of the function for the given range of the input values
For the function, f(x) = 200·(1.08)ˣ, we have, f(x) = y > 0, for all values of x
3) The y-intercept is the value of y, when x = 0, given as follows;
y intercept = f(0) = 200·(1.08)⁰ = 200 × 1 = 200
4) The asymptote is the line that the function approaches but never reaches
In the question, as x tends to -∞, the function f(x) approaches 0. Therefore, f(x) = y = 0 is the asymptote of the function
5) The growth rate of an exponential function, y = a(1 + r)ˣ is r
Therefore, for the function, 200·(1.08)ˣ, which is equivalent to 200·(1 + 0.08) ˣ, the growth rate = 0.08
6) The growth factor of an exponential function, y = a(1 + r)ˣ is (1 + r)
Therefore, for the function, 200·(1.08)ˣ, which is equivalent to 200·(1 + 0.08) ˣ, the growth factor = (1 + 0.08) = 1.08
7) The end behavior as x tends to -∞, [tex]f(x) = y= 200 \cdot (1.08) ^{-\infty} \rightarrow 0[/tex]
8) The end behavior as x tends to +∞, [tex]f(x) = y= 200 \cdot (1.08) ^{-#+\infty} \rightarrow + \infty[/tex]
The texts that complete the blanks are:
Domain: -∞ < x < +∞Range: y > 0y intercept: (0, 200)Asymptote: y = 0The growth rate; r = 0.08The growth factor = 1.08End Behavior: As x → -∞, f(x) → 0End Behavior: As x → +∞, f(x) → +∞The domain
The domain of an exponential function is all set of real numbers.
So, the domain is: -∞ < x < +∞
The range
The range of an exponential function is always greater than 0.
So, the range is y > 0
The y-intercept
This is when x = 0.
So, we have:
[tex]f(x) = 200(1.08)^x[/tex]
This gives
[tex]f(0) = 200(1.08)^0[/tex]
[tex]f(0) = 200[/tex]
So, the y-intercept is (0,200)
The asymptote
This is the line that is close to the function but is not on the function.
The range is:
y > 0.
So, the asymptote is y = 0
The growth rate and the growth factor
The function is given as:
[tex]f(x) = 200(1.08)^x[/tex]
The growth factor is 1.08, while the growth rate (r) is calculated as:
[tex]r = 1.08 - 1[/tex]
[tex]r = 0.08[/tex]
Hence, the growth rate is 0.08, and the growth factor is 1.08
The end behavior
The end behavior of an exponential growth function is:
a x → -∞, f(x) → 0 and as x → +∞, f(x) → +∞
Read more about exponential function at:
https://brainly.com/question/11464095
Related Questions
help!!! which is the correct answer
Answers
Answer:
There are no solutions
Step-by-step explanation:
Answer:
the answer is B;
Step-by-step explanation:
5x-4≥12
c.l.t
5x≥12+4
5x≥16
X≥16/5
or
3,1/5
which is still 16/5
x≥16/5
what is the sum of the exterior angles of a decagon
Answers
Answer:
10 exterior angles of 36° , 10 interior angles of 144° , and 10 vertices
Step-by-step explanation:
The y-intercept of the line whose equation is 2x+y= 4 is 04 0-2 02
Answers
Hope this helps :)
hurry I need the answer in less than 90 min . Which situation represents a non-proportional relationship? 1The cost of purchasing p pounds of salmon for $7.99 per pound. 2 the amount a student makes mowing m number of lawns charging $35 per lawn. 3.The amount of water draining at a rate of 2.5 gallons per minute. 4.The total cost of renting a jet ski for $25 per hour plus a fee of $50.
Answers
Answer:
The Answer is B
Step-by-step explanation:
I just did the test
Answer:
b
Step-by-step explanation:
Simplify 6z^-7 (2) x² (4) ^4x^-4
Answers
Answer:
3
Step-by-step explanation:
Step-by-step explanation:
First, subtract
7
from each side of the equation to put the equation in standard form:
x
2
+
4
x
+
4
−
7
=
7
−
7
x
2
+
4
x
−
3
=
0
We can now use the quadratic formula to find the solutions for
x
. The quadratic formula states:
For
a
x
2
+
b
x
+
c
=
0
, the values of
x
which are the solutions to the equation are given by:
x
=
−
b
±
√
b
2
−
(
4
a
c
)
2
⋅
a
Substituting:
1
for
a
4
for
b
−
3
for
c
gives:
x
=
−
4
±
√
4
2
−
(
4
⋅
1
⋅
−
3
)
2
⋅
1
x
=
−
4
±
√
16
−
(
−
12
)
2
x
=
−
4
±
√
16
+
12
2
x
=
−
4
±
√
28
2
x
=
−
4
±
√
4
⋅
7
2
x
=
−
4
±
√
4
√
7
2
x
=
−
4
±
2
√
7
2
x
=
−
4
2
±
2
√
7
2
x
=
−
2
±
√
7
Or
x
=
−
2
+
√
7
and
x
=
−
2
−
√
7
The domain of the following relation R {(3, -2), (1, 2), (-1, -4), (-1, 2)} is
A. {-1, 1, 3}
b. {-1, -1, 1, 3}
с. {-4, -2, 2, 2}
d. {-4, -2, 2}
Answers
what is 12x − y = 10 in slope form equation?
Answers
Explanation:
You basically what to get y by itself so-
12x-y=10
You will add y to both sides
12x=y+10
Then subtract ten from both sides
12x-10=y or y=12x-10
explain why n(n-1) must be an even number
Answers
Please help me with this math problem and i will mark u brainliest
Answers
Answer:
202.4 - 27 * 3 Add.
202.4 - 81 Multiply.
121.4 Subtract.
Step-by-step explanation:
I solved it from the "add" step, since you already did the rest. The problem was completed by just following the order of operations: PEMDAS.
PLZ HELP ASAP!!!!!!!!
Answers
Answer:
Step-by-step explanation:
formula for cylinder:V=πr2h
shape of the base: circle
formula for circle: A=πr2
radius: 6.5cm
height: 16cm
V=3.14x6.5^2x16
2122.64cm^3
Answer:
Step-by-step explanation:
The formula for volume a a cylinder is V=pi*r²h
The shape of the base is circular
the formula for area of a circle is A=pi*r²
The radius is 6.5 cm
The height is 16 cm
V=pi x 6.5² x 16
The volume of the cylinder is 2123.72
Hope this helps:)
After 6 hours, 4 inches of snow have fallen. Assume it continues just know at a constant rate complete the table to show how much snow have fallen after 1,2,6 and 8 hours
Answers
Answer:
Step-by-step explanation:
For 6 hrs and 4 inches that's 2/3 an inch for every hr
1 hr 2/3 inches
2 hrs 1.3 or 1 1/3 inches
6 hrs 4 inches
8 hrs 5.3 or 5 1/3 inches
The number of students, SSS, serviced by the school system in the town of Emor, ttt years from 2000 can be modeled by the function S(t)=10{,}000(1.1)^t. The number of classrooms, C, in the town of Emor, t years from 2000 can be modeled by the function C(t)=450+40t. Let D be the average number of students per classroom in Emor's school system t years from 2000.
Answers
Answer:
The formula of D (t) is .1000.(1.1)/45+4t
Step-by-step explanation:
The expression representing the number of students serviced by the school system in the town of Emor, t years from 2000 is:
And the expression representing the number of classrooms in the town of Emor, t years from 2000 is: s(t)=10,000.(1.1)^t
The expression D (t) represents the average number of students per classroom in Emor's school system t years from 2000.
Then the average number of students per classroom can be computed by:
C(t)=450+40t.
Average number of students/classroom = Number of students/Number of classrooms so the answer is D (t) .1000.(1.1)/45+4t
Thus,the formula of D (t) is .
What is the slope of the lined graphed above?
-2
-1
-1/2
1/2
2
Answers
(0-1)/(2-0) = -1/2
The slope is -1/2
Answer: D. 1/2
Step-by-step explanation:
5 x 10-2 Standard notation
Answers
Answer:
50x-2
Step-by-step explanation:
(PLEASE ANSWER!) Two distinct lines, L and M, are each perpendicular to the same line N. What is the measure of the angle where line L meets line N? What is the measure of the angle where line M meets line N?
Answers
Answer:
90 and 90
Step-by-step explanation:
If they are perpendicular it means they cross at a 90 degree angle so since both L and M are perpendicular to N both the answers would be 90
Hope This Helps :)
The measure of the angle where line L meets line N is 90° ;
and the measure of the angle where line M meets line N is 90°.
What are perpendicular lines?In geometry, perpendicular lines are defined as two lines that meet or intersect each other at right angles (90°).
Now it is given that,
Two distinct lines, L and M, are each perpendicular to the same line N.
Line L is perpendicular to line N.
Since angle between two perpendicular lines = 90°.
So, angle between line L and line N = 90°
Similarly, Line M is also perpendicular to line N.
Therefore, angle between line M and line N = 90°
Thus, The measure of the angle where line L meets line N is 90° ;
and the measure of the angle where line M meets line N is 90°.
To learn more about angles :
https://brainly.com/question/13524681
#SPJ6
If Kara cuts 2 pounds of cheese into blocks that each weigh
1
3
pound, how many blocks of cheese will she make?
blocks
Answers
The radius of a circle is 12 in. Find its area in terms of \piπ.
Answers
Answer:
pi144
Step-by-step explanation:
square the radius but dont multiply by pi because the question wants you to leave it out.
The slope of the line that represents the data Nicholas collected is -63, and the y-intercept is 825. Explain what these represent in the context of the situation. Remember that x is the number of days, and y is the number of canned goods. The slope of the line that represents the data Nicholas collected is -63, and the y-intercept is 825. Explain what these represent in the context of the situation. Remember that x is the number of days, and y is the number of canned goods.
Answers
Answer:
slope of - 63 in the context means, as the number of days increases by 1, The number of canned goods there is 63 reduction in yhe number of canned goods.
An intercept value of 825 means the Number of canned goods even when the number of days is 0.
Step-by-step explanation:
Given that:
Slope = - 63
y intercept = 825
x = number of days
y = number of canned goods
From the general form of a linear model :
y = mx + c
m = slope / gradient ; c = intercept
Hence,
y = - 63x + 825
A slope of - 63 in the context means, as the number of days increases by 1, The number of canned goods there is 63 reduction in yhe number of canned goods.
An intercept value of 825 means the Number of canned goods even when the number of days is 0.
Answer:
The slope indicates that the soup kitchen uses 63 cans per day. The y-intercept shows that there were initially 825 cans at the soup kitchen.
Step-by-step explanation:
need help asap dont know how to do it
Answers
x equal??
helppp plssss
Answers
Answer:
ngghhjjhgifiufigfigiufuff
Answer:
X=4
Step-by-step explanation:
Emily has a babysitting job that pays $11 per hour. She wants to know how many hours she has to babysit to afford a
new iPad that is $165. Which equation will represent this situation with h representing the number of hours Emily
has to babysit?
Oь
165 = 11 -
165 = 11 +h
165 = 11/h
165 = 11h
с
Od
Review Answers
Saved at 7:52 am
Answers
Answer: 165=11h
Step-by-step explanation:
I believe it would be 165=11h because you have to multiply the number of hours she worked times 11 to get the amount that would equal 165!
PLZ HELP..8TH TIME POSTING :)) yeahhhh
Which algebraic rule describes the transformation?
Wont let me copy and paste picture .-.
Cordinates: RUST: R= -4,-1 U= -4,-3 S= -1,-1 T= -1,-3
Cordinates: R'U'S'T': R'= 4,1 U'= 4,3 S'= 1,1 T'= 1,3
A: (x,y)-----(-x,y)
B: (x,y)-----(-x,-y)
C: (x,y)-----(-y,-x)
Answers
Answer:
B
Step-by-step explanation:
Identifying the domain and range of the relation.
Answers
Answer:
1. The domain is (-2, -1, 0, 1) the rage is (4,2,0,2) 2. It is a function
Step-by-step explanation:
The domain in a pair is always the first number. The range is always the second number in the ordered pair.
Answer:
Domain: {−2,−1,0,1}
Range: {0,2,4}
Step-by-step explanation:
The domain is all the x-coordinates, but NEEDS TO BE ORDERED, which are {−2,−1,0,1} and you also need to include the curly brackets { }.
The range is all the y-coordinates and also NEEDS TO BE ORDERED, which are {0,2,4} and you also still need to include those curly brackets { }.
Hope this helps and answers your question! :)
I accidentally fell asleep in math, I just need yes and no's please help me out!
Answers
Answer:
No, yes, yes, yes, no, no, yes, no, yes, no, no, yes
Step-by-step explanation:
Explanation is in the comments by the way.
Find the area of the trapezoid,
6 in.
4 in.
8 in.
7
The area is
square inches
Answers
Answer:
I think the answer is 8 inches
What is the equation of the line with a slope of 3 and a y-intercept of -2, written in slope intercept form?
Answers
Answer:
y=3x-2
Step-by-step explanation:
Slope intercept form is
y=mx+b
m=slope
while
b=y-intercept
So you replace the variable with the number that is equal to it:
(A variable is a letter that is unknown like m and b)
y=3x-2
Hope this helps!
Answer:
y = 3x -2
Step-by-step explanation:
formula: y =mx+b, m is slope
Jenny is having a party. She has one
large container of soda with 179 ounces in it. A second container holds
128 ounces, but half of it has already
been used. If there are 12 people at
the party, how much soda can each
person have?
Answers
Good luck
Which of these triangle pairs can be mapped to each other using a single reflection?
Triangles F E G and F G L are congruent. Triangle F E G is reflected across line F G to form triangle F G L.
Triangles F E G and G L M are congruent. Triangle E F G is rotated about point G to form triangle G L M.
Triangles F E G and L M N are congruent. Triangle F E G is shifted down and to the right to form triangle L M N.
Triangles L M N and E F G are congruent. Triangle F E G is reflected across a line to form triangle L M N. Triangle L M N is also slightly higher and to the right of triangle E F G.
Answers
Answer:
the first answer (A)
Step-by-step explanation:
took it on edge 2020 (:
Answer:
A
Step-by-step explanation:
I took it on edg 2020 and got it wrong so I thought I would help you
Which graph shows a function where f(2)= 4?
idk i guessed and got it right :)
Answers
Answer:
The 4th graph.
Step-by-step explanation:
Answer:
The first one
Step-by-step explanation:
f(2)=4 means when x=2. F(x) or you may call it y, equals 4, so find the one that when x=2, y=4, then its your answer.
Janet collected 4 times as many bags of cans as her friend. If her friend collected 0.87 of a bag,
how much did Janet collect?
Answers
Answer:
Janet collected 3.48 bags of cans
Step-by-step explanation:
The answer is 3.48 because 0.87 multiplied by 4 is 3.48
Answer:
.384
hope this helps!