What is the asymptote of the graph of an exponential growth or exponential decay function? Explain your reasoning.
Answers
Let's consider an exponential decay function.
As an example, let's look at [tex]f(\text{x}) = 100(0.5)^{\text{x}}[/tex]
Here is a table of selected values:
[tex]\begin{array}{|c|c|} \cline{1-2}\text{x} & \text{f(x)}\\\cline{1-2}0 & 100\\\cline{1-2}1 & 50\\\cline{1-2}2 & 25\\\cline{1-2}3 & 12.5\\\cline{1-2}4 & 6.25\\\cline{1-2}5 & 3.125\\\cline{1-2}6 & 1.5625\\\cline{1-2}\end{array}[/tex]
As x gets bigger, y = f(x) is slowly approaching y = 0. It will never get to this exact value because we keep taking half of the previous y value (eg: we go from y = 25 to y = 12.5); there's no way to arrive at zero through this continuous halving process. If x/2 = 0, then x itself must be 0. But we started off with a nonzero value.
Visually, the curve is slowly approaching the x-axis. We say that the horizontal asymptote is y = 0 which is directly overlapping the x-axis. Think of the asymptote as an electric fence you can get closer to but not actually touch.
See the graph below. I used Desmos to create the graph.
Related Questions
What is the perimeter of a rectangle with a length of Eight and one-sixth feet and a width of Six and two-thirds feet?
Fourteen and three-ninths feet
Sixteen and two-sixths feet
Twenty-nine and four-sixths feet
Forty-eight and three-eighteenths feet
Answers
Answer:
Fourteen and three ninthn feet
Step-by-step explanation:
Just add them together and you get the answer.
Answer: Twenty-Nine and Four-Sixths feet
Step-by-step explanation:
Perimeter is the sum of all sides.
So we just add 8 1/6 + 8 1/6 + 6 2/3 + 6 2/3
but before we can add them up we need to make our fractions have the same denominators
so we multiply the 2/3 by 2 to give us 4/6 then we can add the fractions together
1/6 + 1/6 + 4/6 + 4/6 = 10/6 or 1 4/6
then add 8 + 8 + 6 + 6 + 1 4/6 = 29 4/6 feet
Model each pair of situations with exponential functions f and g. Find the approximate value of x that makes f(x) = g(x).
25. F: initial value of 100 decreasing at a rate of 5%
G: initial value of 20 increasing at a rate of 5%
Answers
The model of the exponential functions
25:
f(x) = 100(0.95)ˣg(x) = 20(1.05)ˣf(x) = g(x) at x = -46.5326
f(x) = 40(1.25)ˣg(x) = 10,000(0.84)ˣf(x) = g(x) at x = 113.11How to model each pair of the functions with exponential functionConsidering the given problem, f(x) = a(b)^x
the starting = a
the base = b
the exponents = x
25.
F: initial value of 100 decreasing at a rate of 5%
a = 100, rate, r = 5%, b = 1 - 0.05 = 0.95
f(x) = 100(0.95)ˣ
G: initial value of 20 increasing at a rate of 5%
a = 20, rate, r = 5%, b = 1 + 0.05 = 1.05
g(x) = 20(1.05)ˣ
solving for f(x) = g(x)
20(1.05)ˣ = 100(0.92)ˣ
divide through by 20
(1.05)ˣ = 5(0.92)ˣ
x㏒(1.05) = ㏒(5 + (0.92)ˣ)
x㏒(1.05) = ㏒5 - x㏒0.92
x㏒(1.05) + x㏒0.92 = ㏒5
-0.015x = ㏒5
x = -46.53
26.
f: initial value of 40 increasing at a rate of 25%
a = 40, r = 25%, b = 1 + 0.25 = 1.25
f(x) = 40(1.25)ˣ
g: initial value of 10,000 decreasing at a rate of 16%
a = 10,000, r = 16%, b = 1 - 0.16 = 0.84
g(x) = 10,000(0.84)ˣ
solving for f(x) = g(x)
40(1.25)ˣ = 10,000(0.84)ˣ
divide through by 40
(1.25)ˣ = 250(0.84)ˣ
x㏒(1.25) = ㏒(250 + (0.84)ˣ)
x㏒(1.25) = ㏒250 - x㏒0.84
x㏒(1.25) + x㏒0.84 = ㏒250
0.0212x = ㏒250
x = 113.11
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consider the decimal -0.022 . what is the decimal as a simplified fraction?
could you also explain how you got your answer you dont have to but it would be helpful :))))
Answers
Answer:
-11/500
Step-by-step explanation:
-0.022
To change the decimal number into a fraction, start by reading the number.
The second 2 is in the thousandths place. This number is read as:
"negative twenty-two thousandths"
Now write a fraction with 22 over 1000, and with a negative sign.
-0.022 = -22/1000
Now we reduce. 22 and 1000 are divisible by 2.
-0.022 = -22/1000 = -11/500
i used my calculator and put the decimal into it and hit equal and then presses the button above the equal sign that looks like < > and then hit the button that says simp
Can someone help, please
Answers
Answer:
- 8/7
Step-by-step explanation:
slope = (13-5)/(3-10)
slope = 8/-7
slope = - 8/7
Which of the following tables represents a linear relationship that is also proportional?
x −1 2 5
y −1 0 1
x −2 −1 0
y −1 0 1
x −2 −1 0
y −4 −2 0
x −4 −2 1
y −2 0 3
Answers
————————————————
Write the inequality shown by the graph.
Answers
hope this helped :)
A store is instructed by corporate headquarters to put a markup of 11% on all items. An item costing $18 is displayed by the store manager at a selling price of $2. As an employee, you notice that this selling price is incorrect. Find the correct selling price. What was the manager's likely error?
(Round to the nearest dollar as needed.)
Answers
Answer: The amount off is 1.98 which means the the correct price is $16.02
Step-by-step explanation: 18 x 11 = 198 divided by 100 = 1.98 subtract 1.98 from 18 and boom you have the correct discounted price
Two questions added in both images.
Answers
Answer:
17.876
Step-by-step explanation:
my math teacher Mr.Q
Hope this helped!!!!!!
please help?! ...i don't understand
Answers
Answer:
16.449 = 16.4
9.84 = 9.8
by estimating = 26.2
Answer:
16.5+9.8=26.3
Step-by-step explanation:
The equation is 16.449+9.84. We need to add these together after we round them to the nearest tenth. Well with decimals it goes ones, tenths, hundreths. So The second number past the decimal on the right side, is the one that we are rounding. If the number is greater than 5 then we move the number to the next tenth value.If its less than f5 we do the complete opposite.
16.449 is going to be rounded to be 16.5.
9.84 is going to be rounded to be 9.8
Now that our numbers are rounded we can add them.
16.5+9.8=26.3
I hope this helps!!!
Any additional help with rounding to the nearest tenth you could, if you want, use the website nearesttenth.com (Just to help you, I don't work with that website and not trying to advertise it like that).
A student earned the scores in the data set in one course. {78, 64, 74, 92, 67} What is the mean of the scores?
Answers
Answer: The mean is 75
Step-by-step explanation:
- You add the scores in the data:
78+64+74+92+67 = 375
- Then divide by the number of scores in the data:
there are 5 scores in the data,
1) 78
2) 64
3) 74
4) 92
5) 67
- So:
375/5 = 75 <--- mean
To calculate mean or average from a data set, add all the data points together and then divide by the number of points you added together.
In this case,
78+64+74+92+67= 375/5= 75
<3
Compare each investment to an investment of the same principal at the same rate compounded annually.
17. Principal: $8,000
Annual interest: 6%
Interest periods: 4
Number of years: 20
Answers
Step-by-step explanation:
income is based on a formula (rt)
r is a % of p (% being Annual Interest)
t is time (number of years)
p is principal.
17. 9,600$ in interest (lost or gained, gained is added from p, lost is subtracted from p)
18. is 1,750$
I am not entirely sure what interest periods are but I assume you can use this formula to find it. good luck man.
Write an exponential function to model the data in each table. Identify the growth or decay factor. (23) Picture
Answers
The model of the exponential functions show that
23: table 1 is a decay with a rate of 50%24. tables 2 is a growth with a rate of 10%How to write exponential function to model the data in each tableConsidering the given problem, f(x) = a(b)^x
the starting = a
the base = b
the exponents = x
23. Table 1
At x = 0
f(x) = a(b)^x
(b)^0 = 1
solving for a
4 = a * (b)^0
4 = a
At x = 1
f(x) = a(b)^x
(b)^1 = b
substituting known variables
2 = 4(b)^1
b = 2/4
b = 0.5
for decreasing rate, b = 1 - 0.5 = 0.5
rate, r = 50%
24. Table 2
At x = 0
f(x) = a(b)^x
(b)^0 = 1
solving for a
100 = a * (b)^0
100 = a
At x = 1
f(x) = a(b)^x
(b)^1 = b
substituting known variables
110 = 100(b)^1
b = 110/100
b = 1.10
for increasing rate, b = 1 + r = 1.10, r = 0.10
rate, r = 10%
The base is what determines exponential growth or decay
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Fred bought 4 new baseball cards to add to his collection. The next day his dog ate half of his collection. There are now only 33 cards left. How many cards did Fred start with ?
Answers
We have to work backwards; he has 33 cards left because his dog ate half of his collection. If we multiply 33 and 2 (which will be how much he had BEFORE half was eaten), we get 66. That is after 4 new baseball cards were bought. We need to subtract 4 from 66 in order to see what he originally had, making that 62 cards!
3.
(04.05 LC)
Which of the following inequalities matches the graph? (1 point)
graph of an inequality with a solid vertical line through the point 5, 0 and shading to the left of the line
x ≤ 5
x ≥ 5
y ≤ 5
y ≥ 5
Answers
Answer: The inequality that matches the graph is x ≤ 5. This is because the graph has a solid vertical line at x = 5 and the shading is to the left of the line. This indicates that all values of x that are less than or equal to 5 satisfy the inequality.
The inequality x ≥ 5 would not match the graph because the shading would be to the right of the line. The inequalities y ≤ 5 and y ≥ 5 do not match the graph because they are not in the correct form. Inequalities involving y have a graph with a horizontal line, not a vertical line.
PLS HELP!!!! The revenue for a local photographer for the month is $1200. His costs include a studio rental of $600, props costing $105, materials fees of $115, and a make-up artist who charges $130. What is his total profit for the month?
Answers
Answer: $250 profit
Step-by-step explanation:
600+105+115+130 = 950
1200 - 950 = $250 total profit
1200-600-130-115-105
Blanca is going to use a box that is a rectangular prism for a card box at her son’s birthday party. She will wrap and decorate the box. The dimensions of the box are shown in the diagram.
What is the total surface area of the box in square inches?
Answers
Answer:24 m/s
Step-by-step explanation:
(-1/3)⁴(-1/3)²
help please
Answers
what is the value of this expression
5 (9/12 - 1/4) + 0.5
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The answer to this is 3
__________________________________________________________
PEMDAS= Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction
__________________________________________________________
9/12 - 1/4 = 0.5
0.5 x 5 = 2.5
2.5 + 0.5 =3
Find the sum of 5.21 × 1019 and 3.149 × 1017.
8.359 × 1019
5.24149 × 1019
5.24149 × 1036
8.359 × 1036
Answers
Answer: 8511. 523
Step-by-step explanation:
Re write the equation:
(5.21 x 1019) + (3.149 x 1017)
= 8511. 523
Please answer all of them and I will give brainlest
Answers
2) m=2 b=10, y=2x+10, non, positive
3)m=44 b=48, y=44x+49, non, negative
I can't do the last one
on Monday, Gina ran 1 mile in 9.3 minutes. her times for running 1 mile on each of the next four days, relative to her time on Monday, were -1 2/3 minutes, -1.45, -1.8 minutes and - 1 3/8 minutes. list these relative times in order from least to greatest?
PLEASE HELP THIS WAS DUE FRIDAY BUT I DIDNT HAVE TIME
THANK YOU FOR YOUR HELP
Answers
Answer:
-1.8 < 1 2/3 < 1.45 < 1- 3/8 < 9.3
Step-by-step explanation:
-1 2/3= -1.67 min
-1 3/8 = -1.375 min
so 7he least to greatest is
-1.8 < 1 2/3 < 1.45 < 1- 3/8 < 9.3
The ordered list from least to greatest is -1.8 < -1 2/3 < -1.45 < -1 3/8
What is a mixed fraction?
A fraction represented with its quotient and remainder is a mixed fraction. For example, 2 1/3 is a mixed fraction, where 2 is the quotient, 1 is the remainder.
So, a mixed fraction is a combination of a whole number and a proper fraction.
According to the given question:
Gina's relative time list is [tex]-1\frac{2}{3}[/tex] , -1.45, -1.8, [tex]-1\frac{3}{8}[/tex]
Converting mixed fractions to decimal forms to make comparison easy.
-1 2/3 = -1 + 2/3 = - 1.6 min
-1 3/8 = -1 + 3/8 = -1.375 min
Hence the new list is - 1.6, - 1.45, - 1.8, - 1.375
Arranging from least to greatest as follows
-1.8 < - 1.6 < - 1.45 < - 1.375
- 1.8 < -1 2/3 < -1.45 < -1 3/8
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Charles is in charge of cooking broccoli and zucchini for a large group. He has to spend all $20.10 he has and can carry 11 pounds of veggies. Zucchini costs $1.60 per pound and broccoli costs $2.10 per pound. How many pounds each of zucchini and broccoli can Charles get so that he spends all $20.10 and gets 11 pounds of veggies? Let x represent the number of pounds of zucchini and y represent the number of pounds of broccoli. Show ALL work!
Answers
Answer:
Total equation: X + Y = 11 pounds
Cost equation: 1.60X + 2.10Y = 20.10
Number of Pounds of Zucchini = 6
Number of Pounds of Broccoli = 5
Step-by-step explanation:
You get the equations by just pulling the information from the text.
We then take the total equation and rearrange it to solve for one of our values. I will be using X
X + Y = 11 so first subtract X from both sides to get
Y = 11 - X so now we know what Y equals
next take the cost equation and input X in wherever it shows up so
1.60 (X) + 2.10 (11 - X) = 20.10
now distribute 2.10 to the values in the parathesis to get
1.60X + 23.1 - 2.10X = 20.10
now combine like terms
-0.5X + 23.1 = 20.10
now subtract 23.1 from both sides
-0.5X = -3
now divide both sides by -0.5
X = 6
so now we know that he both 6 pounds of zucchini now plug that into the total equation
6 + Y = 11
subtract 6 from both sides
Y = 5
(-10) to the 6th power
Answers
Answer:1000000
Step-by-step explanation:
Raise -10 to the power of 6
(-10)(-10)(-10)(-10)(-10)(-10)
1000000
since there is a parentheses around -10 and the power is a even number, the answer is positive.
Write the inequality shown by the graph.
Answers
Answer: X<1 1/2
Step-by-step explanation:
Find the missing number/s so that the equation has One solution.
__x + 3 = –4x + 17
Select all that apply
A: -4
B: 5
C: 2
D: 7
Answers
Answer:
Step-by-step explanation:
D) -10 = -28 + 17
ANS:- -10 = -10
The slope of the line that passes through the point \left( 2 , 4 \right)(2,4) and \left( 3 , 8 \right)(3,8) is
Answers
Answer:
Step-by-step explanation:
tbh im confused
Question 9 math homework
Answers
Answer:
D
Step-by-step explanation:
Things To Keep In Mind:
a^2 + b^2 = c^2 (Pythagorean Theorem)
C^2 is usually the hypotenuse or the slanted side across from the right angle
(The right angle is 90 degrees and is marked with a square)
a and b can be switched around
a=5
b=?
c=10
5^2+b^2=10^2
5^2=25
10^2=100
25+b^2=100
-25 -25
b^2=75
b=square root of 75
The answer is D
If there is a problem with this answer please feel free to tell me, thanks :)
Three subtracted x from is greater than or equal to -25.
Answers
You subtract 3 from -25
Can someone help, please
Answers
Answer:
Y=8x+9
Step-by-step explanation:
I hope this helped you
Can someone help, please
Answers
Answer:
9/5
Step-by-step explanation:
Slope=(y2-y1)/(x2-x1)
(10-1)/(7-2)
=9/5
(I’m sorry if that is incorrect, hope it helped)