Answers
Part 1) Finding the inverse
Let x = r and y = H(r)
We have the equation y = 6240(1 + x/100)^t which is the same as saying y = 6240(1 + 0.01x)^t since 1/100 = 0.01
From here, swap x and y to get the equation x = 6240(1+0.01y)^t
Let's solve for y
x = 6240(1+0.01y)^t
6240(1+0.01y)^t = x
(1+0.01y)^t = x/6240
1+0.01y = (x/6240)^(1/t)
0.01y = (x/6240)^(1/t)-1
100*0.01y = 100*((x/6240)^(1/t)-1)
y = 100*((x/6240)^(1/t)-1)
y = 100*(x/6240)^(1/t) - 100
This becomes r = 100*(H/6240)^(1/t) - 100 after we replace y with r and x with H. Note the r and H swapped places, just like x and y did. Earlier we had H isolated on the left, but now r is isolated on the left.
We could write r(H) = 100*(H/6240)^(1/t) - 100 to mean the same thing.
So what exactly does this inverse function do? Well the original function tells us the number of households for any given growth rate, which is r.
The inverse function swaps things around to allow us to find the growth rate if we know how many households there are. We're working backwards. In both cases, t is held to some constant fixed value.
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Part 2) Finding the growth rate if the number of households is 7800 after 3 years.
We're going to plug in H = 7800 and t = 3 into the inverse function we found to determine the value of r, or r(H)
r(H) = 100*(H/6240)^(1/t) - 100
r(7800) = 100*(7800/6240)^(1/3) - 100
r(7800) = 7.72173450159419
You'll need your calculator to get this approximate value. After rounding to two decimal places, we get r(7800) = 7.72
Since r = 7.72, this means the growth rate is 7.72%
Related Questions
Help meh- im d u m b
Answers
Answer:
[A] 0Explanation:
Lines of symmetry; A line that cuts a shape exactly in halfIf you were to put a line of symmetry down and fold the shape in half on that line, both halves would match exactly.
If you were to put a line of symmetry down on this triangle both sides would not match, therefore there are no lines of symmetry.There are zero lines of symmetry, therefore your answer is [A] 0Mary has a container filled with 20 ounces of cereal. Each day she eats 4.5 ounces
of cereal.
• Write an expression to represent the amount of cereal left after x days.
Answers
Answer:quin hill from ms Henry math class?!?!?!?! Why are you on brainly.....
Step-by-step explanation:3.1
Mrs Jenkins buys a car for £3400.
She sells it for £3800.
Work out her percentage profit.
Answers
Answer:
%11.76
Step-by-step explanation:
400/3400x100 = 11.76
A ball is projected upward from ground level. After t seconds, it’s height in feet is a function defined by f (t) = -16t^2 + 96t. In how many seconds will the rocket be at a height of 128 ft above the ground?
Answers
Answer:
t = 2 s and t = 4 s
Step-by-step explanation:
A ball is projected upward from ground level. After t seconds, it’s height in feet is a function defined by,
[tex]f (t) = -16t^2 + 96t[/tex]
We need to find in how many seconds will the rocket be at a height of 128 ft above the ground.
It means,
[tex]128= -16t^2 + 96t\\\\-16t^2+96t-128=0\\\\16(-t^2+6t-8)=0\\\\(-t^2+6t-8)=0\\\\-t^2+4t+2t-8=0\\\\t(-t+4)-2(-t+4)=0\\\\(t-2)=0\ and\ (-t+4)=0\\\\t=2\ and\ t=4[/tex]
So, it will be at a height of 128 feet at 2 second and 4 second.
2 Which of the following fractions are equivalent to 2/4?
Answers
Answer:
1/2=2/4
Step-by-step explanation:
help i need help i really really need help no cap
Answers
your welcome
ABOVE & BEYOND: What is the slope of the line graphed below?
Answers
Answer:
3
Step-by-step explanation:
The diameter of a circle is 40.0cm. What is the circumference of the circle?
Use 3.14 for pi
Help would really be appreciated bc I do not understand circles lol
Answers
Answer:
Answer is 125.6
Step-by-step explanation:
Diameter=40cm
radius=40÷2 = 20cm
Circumference = 2πr
=2×3.14×20
=125.6
Paul invests £150 in a bank account paying 2% interest per annum for 10 years. Work out how much money he has in the account at the end of the 10 years
Answers
Answer: £180
Step-by-step explanation:
The interest gotten for the 10 years will be calculated as:
= Principal × Rate × Time
= 150 × 2% × 10
= 150 × 0.02 × 10
= 30
The amount he has in the bank account at the end of the 10 year will be:
= Principal + Interest
= £150 + £30
= £180
density of the cube is 9.86 g/cm³ and the volume is 150cm³ work out the mass in kg
Answers
Mass= Density *Volume
9.86 g/cm3 *150 cm3 =1479g
1479 g to kilograms
1479g= x
1000g = 1 kg
x = 1479 g / 1000 x = 1.479 kg.
Can you help me please?
Answers
Answer:
yes
Step-by-step explanation:
you can use the vertical line test- for every line going up and down there should only be one point. if there is one and only one, it's a function. if there are more than one per line, then it is not a function.
Write and solve an inequality to find the values of x for which the perimeter of the rectangle is less than 136.
The diagram says x+4 on the top and x on the side
please help me solve this thanks
Answers
Answer: 4x+8<120
x<28
Step-by-step explanation:
As per the statement in the question, the inequality will be 4x + 8 < 136.
What is inequality?Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare the two values. Less than (or less than and equal to), larger than (or greater or equal to), or not similar to signs are used in place of the equal sign in between.
As per the instructions given in the question,
The length (l) of the rectangle = x+4
The width (w) of the rectangle = x
As per the formula of the perimeter, P:
P = 2 (l + w) (i)
Put the values in (i)
P = 2 (x + 4 + x)
P = 2x + 8 + 2x
P = 4x + 8
Then the inequality as per the statement in the question will be,
4x + 8 < 136.
To know more about inequality:
https://brainly.com/question/28823603
#SPJ2
A cinema has 300 seats. 60% are filled. How many are empty? i will give brainliest
Answers
............
Answer:
120 seats
Step-by-step explanation:
Total seats in the hall = 300
Percentage of filled seats = 60 %
Number of seats filled = (60 / 100) 300
= 60 * 3
= 180
Therefore, number of empty seats = 300 - 180
= 120
Hope it helps :)
Please mark my answer as the brainliest
Theo earned £15400 last year and spent 6% of his money on making home improvements. Find how much money Theo spent on home improvements last year.
Give your answer to the nearest penny.
Answers
Answer:
15400 ÷ 6/100
Step-by-step explanation:
next step do yourself
I hope it will help you
Y=4-2x 3y-2x=4 solve using substitution
Answers
Answer:
x=1 y=2
Step-by-step explanation:
y=4-2x 3y=4+2x
3*(4-2x)=4+2x
12-6x=4+2x
12-4=2x+6x
8x=8
x=1
y=4-2*1
y=2
What is the simplest form of of this expression?
Answers
Answer:
B
Step-by-step explanation:
Plssss help meee I need help
Answers
Answer:
no
Step-by-step explanation:
[tex]29^{2} \neq 20^{2} + 26^{2}[/tex]
Kathy wants to paint the faces of her standard six-sided die so that each face is either red or blue. However, she does not want all of the faces to be the same color. How many ways are there for Kathy to paint her die?
Answers
Answer:
The number of ways Kathy can paint her die is 52 ways
Step-by-step explanation:
The permutation and combination related question is answered as follows;
The number of faces in the six-sided die = 6
The number of colors available for painting the six-sided die = 2 colors
Therefore, we have, the total number of ways Kathy can paint her die, 'n', given as follows;
n = ₆P₂ + 2₄P₄ + 2₄P₃ + ₄P₂
Where;
₆P₂ = The number of ways of arranging 2 objects in 6 spaces = 30
₄P₄ = The number of ways of arranging 4 objects in 4 spaces = 1
₄P₃ = The number of ways of arranging 3 objects in 4 spaces = 4
₄P₂ = The number of ways of arranging 2 objects in 4 spaces = 12
∴ n = 30 + 2×1 + 2×4 + 12 = 52
The number of ways Kathy can paint her die, n = 52 ways.
Simplify 5a – (2a + 6)
Answers
Answer:
Step-by-step explanation:
Add '-2a' to each side of the equation.
5a + -2a = -6 + 2a + -2a
Combine like terms: 5a + -2a = 3a
3a = -6 + 2a + -2a
Combine like terms: 2a + -2a = 0
3a = -6 + 0
3a = -6
Divide each side by '3'.
a = -2
Simplifying
a = -2
5a -2a -6
3a -6
Step-by-step explanation:
..........................
The average cost for a gallon of gasoline in 2006 was $2.45. In 2007, the average cost of a gallon of gasoline was $3.29. What is the approximate percent of change in the cost of a gallon of gasoline?
A. 25%
B. 35%
C. 75%
D. 135%
Answers
Answer:B
Step-by-step explanation:
2.45(0.35)= 0.8575+2.45= 3.30
This block of ice needs to be wrapped in a special reflective material to keep it from melting before the ice carving competition begins. How much reflective material is needed to cover the block completely, with any overlaps?
Question 5 options:
3.1 m2
1.144 m2
3.67 m2
6.7 m2
Answers
Someone plz help me with this 2 questions I will give brainliest
(Look at the pictures)
Answers
Answer:
61 ounces
Step-by-step explanation:
1 pound = 16 ounces
8 pound 3 ounces = 8*16 + 3 = 128 +3 = 131 ounces
No Jesse's weight = 12 pounds = 12*16 = 192 ounces
Weight gained = 192 - 131 = 61 ounces
Evaluate 2x when x = 4
COULD SOMEONE HELPP
Answers
x is 4 so 2x4=8
Since x=4
You will multiply 2x
X means 4 basically cause it says what it is equal to then all you do is:
2x4=8
And if you wanna learn more of these types of questions I’ll help you in the comments! (:
Did I do it rightly?
Answers
Help I need this now
Answers
Answer:
There is no question showing up so I dont know how to help u
Step-by-step explanation:
Volume of cylinder & cone ... Help me please
Answers
Answer:
The formula for the volume of a sphere is 4⁄3πr³. For a cylinder, the formula is πr²h. A cone is ⅓ the volume of a cylinder, or 1⁄3πr²h.
The aquarium opened at 8.00 am . In the first hour 140 people purchased admission tickets . In the second hour 25 % more people purchased admission tickets than the first hour . Each ticket cost 15.25 . What was the total amount of money paid for all the tickets purchased in the first two hours please help
Answers
Answer:
Total income= $4,083.75
Step-by-step explanation:
First, we need to calculate the total number of people that enter the aquarium in the first two hours.
1st hour= 140
2nd hour= 140*1.25= 175
Total number of people= 315
Now, we can determine the total amount of money earned:
Each ticket cost 15.25.
Total income= 315*15.25
Total income= $4,083.75
solve using a2 + b2 = c2
show the work please :)
Answers
Answer: 19.20937
Step-by-step explanation:
a2=15
b2=12
c2=?
a2+b2=c2
15(15)+12(12)= c2
225+ 144=c2
√369= √c2
≐19.20937 ft
3√41
find the area of the circle with a cirumfererference of 30pi write your solution in terms of pi
Answers
Answer:
225 pi
Step-by-step explanation:
2pi r=30pi
pi r =15pi
pi r2=225pi
225 pi
State the slope and y-intercept of the graph of y+2x=3
Answers
Answer:
Slope(m)=2x
y-intercept(b)=3
Step-by-step explanation:
Answer:
Slope is -2x, Y-Intercept is 3
Step-by-step explanation:
You need to isolate the "y" to get the answer, all you need to do is subtract the "2x" from both sides
