Answer:
A generic exponential function can be written as:
f(x) = A*e^(b*x)
Where A and b are real numbers, that we need to find.
We know that the points (3, 6) and (7, 18) are solutions to the equation, then we have that:
A*e^(b*3) = 6
A*e^(b*7) = 18
This is a system of equations, to solve this we can take the quotient between the two equations, so we remove the variable A.
(A*e^(b*7))/(A*e^(b*3)) = 18/6
e^(b*7)/e^(b*3) = 3
e^(b*7 - b*3) = 3
e^(4*b) = 3
Now we can apply the Ln(x) to both sides, because:
Ln(e^y) = y
then:
Ln(e^(4*b)) = Ln(3)
4*b = Ln(3)
b = Ln(3)/4
Then we have:
f(x) = A*e^(Ln(3)/4*x)
And we can use one of the equations to find the value of A. for example:
6 = A*e^(Ln(3)/4*3)
6/e^(Ln(3)/4*3) = 2.632
Then the exponential function is:
f(x) = 2.632*e^(Ln(3)/4*x)
Then we have that:
f(20) = 2.632*e^(Ln(3)/4*20) = 639.576
Rounding to the next integer, we have:
f(20) = 640
An exponential function can represent growth or decay.
The value of f(20) is 673
An exponential function is represented as:
[tex]y = ab^x[/tex]
At point (3,6), we have:
[tex]6 = ab^3[/tex]
At point (7,18), we have:
[tex]18 = ab^7[/tex]
Divide both equations
[tex]\frac{18}{6}= \frac{ab^7}{ab^3}[/tex]
[tex]3= b^4[/tex]
Take 4th roots of both sides
[tex]\sqrt[4]{3}= b[/tex]
Rewrite as:
[tex]b = \sqrt[4]{3}[/tex]
[tex]b = 1.32[/tex]
Substitute 1.32 for b in [tex]6 = ab^3[/tex]
[tex]a(1.32)^3 = 6[/tex]
[tex]2.30a = 6[/tex]
Divide both sides by 2.3
[tex]a = 2.61[/tex]
So, the function is:
[tex]y =2.61(1.32)^x[/tex]
When x = 20, we have:
[tex]y =2.61(1.32)^{20[/tex]
[tex]y =673[/tex]
Rewrite as:
[tex]f(20)=673[/tex]
Hence, the value of f(20) is 673
Read more about exponential functions at:
https://brainly.com/question/11464095
5
4 cm
4 cm
2 cm
6 cm
Help! I will give the Brainly
Answer:
sry i hope u find what your looking for
Find the value of c that completes the square
x^2-x+c
Please help me with how to do this, and show me. Thank you.
Answer:
The value of c is 1/2
Step-by-step explanation:
We have to find the value of c that completes the square [tex]x^2-x+c[/tex]
So, completing square is of form: [tex]a^2-2ab+b^2=(a-b)^2[/tex]
In the question given the value c can be found by breaking the middle term. we are given -x while the general formula is 2ab for middle term so, our c = 1/2 i.e 2(x)(1/2) we get x so, solving:
[tex]x^2-x+c\\=x^2-2(x)(\frac{1}{2})+(\frac{1}{2})^2-(\frac{1}{2})^2\\=(x-\frac{1}{2})^2-(\frac{1}{2})^2[/tex]
The value of c is 1/2
whats 1 + 77 just for you guys to get points :)
Answer:
78 !!!!
Step-by-step explanation:
Use substitution to show that 9+6(10-7x) is equivalent to 69-42x.
Answer:
hope this helps
Step-by-step explanation:
9+6(10-7x)
=9+60-42x
=69-42x
PLEASE HELP, DUE SOON!!
r/n + t=4v solve for r
Answer:
hi
Step-by-step explanation:
r=4vn-tn
List the angles of triangle WXY in order from smallest to largest.
Answer: W, Y, X (choice D)
=======================================================
Explanation:
The square angle marker means angle X is 90 degrees.
For any triangle, the three angles always add to 180
X+Y+W = 180
90+(2x+9)+(2x+1) = 180
4x+100 = 180
4x = 180-100
4x = 80
x = 80/4
x = 20
Use this x value to find the other angles
angle Y = 2x+9 = 2*20+9 = 49
angle W = 2x+1 = 2*20+1 = 41
As a check,
X+Y+W = 90+49+41 = 180
which confirms we have the right angles.
The last step is to sort the angles from smallest to largest
That would lead to W, Y, X which is choice D
A color printer prints 28 pages in 8 minutes.
How many pages does it print per minute?
Answer:
use division
Step-by-step explanation:
this question is pretty simple, all you need to do is the opposite of multiplication, which is........division.
so divide 28 by 8 = 3.5
so it prints 3.5 (3 and a half) pages per minute.
Hi, I'm new can I get marked as brainlieser? It would be highly appreciated.
Hope my answer helps :)
Which of the following could Not be the side length of a right triangle?
Answer:
I think ITS B
Step-by-step explanation:
Hope this helped
-BB
Help ???????????????
Answer:
A
Step-by-step explanation:
use slope formula hope this helps
Zahara mixed 5 quarts of dry ingredients and 2 quarts of water and a batch of concrete .She ran out of the mixture before finishing her project so she made another batch 10 quarts of dry ingredients . How many quarts of water does zahara need to add to keep the consistency the same? Complete the ratio square
Answer: 4 quarts.
Step-by-step explanation:
Given data:
Amount of dry ingredients = 5 quarts.
Amount of water in the mixture = 2 quarts.
Solution:
Let’s a represent the amount of dry ingredients.
Let b represent the amount of water
For first Batch
a/b = 5/2.
b = 2/5a ....... equation 1
For second Batch
a= 10
substitute a into equation 1 to solve for b
b = 2/5(10)
b = 4.
The ratio for batch b = 10/4.
Zahara needs to add 4 quarts of water to the mixture.
Answer:4 quarts!
Step-by-step explanation:
Find the slope of the graph. Write it as a fraction or whole number (not a mixed number).
3/5
all u have to do is find two point and count down and to the side basically find the distance of those two points to find the slope.
Answer:
3/5
Step-by-step explanation:
From what I can see two points of the line are (0,1) and (5,4) so you can just count and do rise/run which is y/x or the formula which is like y^2-y^1/x^2-x^1 they both get the same answer which is 3/5
If you plug the numbers into the formula it gives you 4-1/5-0 which is 3/5
A quadratic function passes through the point (-7, -16) and has a vertex at (-6,
-18). Write the function in the form y = ax2 +bx+c. What are the values of a, b and
c?
Answer:
4 6 7
Step-by-step explanation:
;-;
The consecutive angles of a rectangle are supplementary
a.) Sometimes
b.) Never
c.) Always
Answer:c
Step-by-step explanation:
What is the slope of a line that passes through the points (2,0) and (6,−12)
Answer:
slope = -3
Step-by-step explanation:
Slope formula: [tex]\frac{y2-y1}{x2-x1}[/tex]
Given points: (2, 0), (6, -12)
(2, 0) = (x1, y1)
(6, -12) = (x2, y2)
To find the slope, input the two given points into the formula used to find slope:
[tex]\frac{-12-0}{6-2}[/tex]
Simplify:
-12 - 0 = -12
6 - 2 = 4
[tex]\frac{-12}{4} = -\frac{3}{1}=-3[/tex]
The slope of the line is -3.
Hope this helps :)
Answer my math question I asked so many times I lost most of points by
Answer:
i think 3x+12=7x y
Step-by-step explanation:
I m s o d u m b t h a t i c a n t e v e n d o 1 + 1 s o i n e e d h e l p
Answer:
1 + 1 = 2
Step-by-step explanation:
:)
Answer:
1 + 1 = 2
Hope it Helps
P = $660, R = 9%, T = 2 years
I = ?
((Honestly I don't understand anything, I was busy throwing up while my teacher was showing us how to do it))
Answer:
$ 118.80
Step-by-step explanation:
First, converting R percent to r a decimal
r = R/100 = 9%/100 = 0.09 per year,
then, solving our equation
I = 660 × 0.09 × 2 = 118.8
I = $ 118.80
The simple interest accumulated
on a principal of $ 660.00
at a rate of 9% per year
for 2 years is $ 118.80.
I need to find x and y
2x+4y=8
x=3y-6
Answer:
(x, y) = (0 , 2)
Step-by-step explanation:
Answer:
use elimination or substitution.
Step-by-step explanation:
how many rides can u go on for $10.00 if each ride is $0.25 ?
Answer:
40
Step-by-step explanation:
0.25x40=10 dollars
Pls can someone help me expand:(x+5)(x-8) in quadratic equation
(x + 5)(x - 8)
= x² + {5 + (-8)}x + 5(-8)
= x² - 3x - 40
The area of a circular garden is 121pi
square feet. How much fencing would
be needed to enclose the garden?
Answer:
22 pi ft
Step-by-step explanation:
We can use the area to find the radius
A = pi r^2
121 pi = pi r^2
Divide each side by pi
121 = r^2
Take the square root
sqrt(121) = sqrt(r^2)
11= r
Now we need to find the circumference
C = 2*pi*r
C = 2* pi *11
C = 22 pi ft
Answer:
1. Use area to find radius.
A = π r^2
121 π = π r^2
2. Divide each side by π.
121 = r^2
3. Take in the square root .
[tex]\sqrt{121} = \sqrt{r^{2} }[/tex]
11 = r
4. Find the circumference .
C = 2 × π × r
C = 2 × π × 11
C = 22 π ft
Write n times 7 as an expression
Answer:
7n
Step-by-step explanation:
Answer:
n x 7
Step-by-step explanation:
hope this helps
I need help with solving this problem please I will mark brainliest if correct !!!
Answer:
Supplementary angles
Step-by-step explanation:
The 2 angles are same- side interior angles and are supplementary
Find the distance between A and B .
Answer:
2 and 6/10 or 2 and 3/5
Step-by-step explanation:
qazxwsdcerfvtbgynhumjilkop
Answer:
2 and 3/5 or 2 and 6/10
Step-by-step explanation:
Count the whole numbers and then count each line all the way till it reaches the whole number. If you can simplify then simplify both numbers by a number that goes in them both.
A total of 202 tickets were sold for a theatre showing. If child tickets cost $6 and adult tickets cost $10, how many tickets of each were sold if the theatre earned a total of $1708.
Answer:
167 adult tickets were sold
35 children tickets were sold
Step-by-step explanation:
Let the number of adult tickets be x
Let the number of children tickets be y
Total number of each ticket sold;
x + y = 202 equation 1
Total cost of the tickets
10x + 6y = 1708 equation 2
Let
x= 202 - y equation 3
Substitute 3 into 2
10(202 - y) + y = 1708
2020 - 10y + y = 1708
-9y = 1708 - 2020
-9y = -312
y= 35
Substitute y =35 into 1
x + 35 =202
x= 202 - 35
x= 167
Therefore;
167 adult tickets were sold
35 children tickets were sold
HELP I HAVE TEN MINUTES!!!!!
Answer:
B
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
hdhddhhskalsk bshshshs
A store buys a camera for $80 and decides to markup the price 35%. How much does the camera sell for?
Step-by-step explanation:
80$ is original price so 100%
markup by 35% make price 135%
crossmultiplication
ans=108
Based on the cost of the camera and the percentage markup, the selling price of the camera is $108.
The camera's selling price is 35% more than its cost price. That 35% is:
= 80 x 35%
= $28
The selling price of the camera is therefore:
= Cost of camera + Increase
= 80 + 28
= $108
In conclusion, the camera is being sold for $108.
Find out more at https://brainly.com/question/3837.
Giving brainliest!!
Find the inverse of function f.
f(x) = 1 - 1
OA ) = 7 - 1 1 2 2 2
OB. 1-1) = 7 - 21:
oc/) = 1 - 1
OD. (I) = 12 - 211
Answer:
Gah! Inverses!
Step-by-step explanation:
This is a pretty simple concept, just switch the x and f(x) values!
If you don't understand, look at how I solve it!
[tex]f(x)=\frac{1}{3} -\frac{1}{21} x[/tex]
Switching the positions of the x and f(x) values...
[tex]x=\frac{1}{3} -\frac{1}{21} f(x)^{-1}\\[/tex]
Note: That f(x)^-1 is the proper notation for inverse functions.
[tex]x-\frac{1}{3} =-\frac{1}{21} f(x)^{-1} \\f(x)^{-1}=-21x+7[/tex]
There you go!
Hope this helps, and don't procrastinate!