Answer:
a) The exponential function is [tex]A(t) = 10083(1.068)^t[/tex]
b)
The balance after 1 year is of $10,768.644
The balance after 2 years is of $11,500.91
The balance after 5 years is of $14,010.25.
The balance after 10 years is of $19,467.15
c)
The doubling time is of 10.54 years.
Step-by-step explanation:
Continuously compounded interest:
The amount of money earning after t years, with interest compounded continuously, is given by:
[tex]A(t) = A(0)(1+r)^t[/tex]
In which A(0) is the amount of the initial investment and r is the growth rate, as a decimal.
a) Find the exponential function that describes the amount in the account after time t, in years.
Suppose that $10,083 is invested at an interest rate of 6.8% per year
This means, respectively, that [tex]A(0) = 10083, r = 0.068[/tex]
So
[tex]A(t) = A(0)(1+r)^t[/tex]
[tex]A(t) = 10083(1+0.068)^t[/tex]
[tex]A(t) = 10083(1.068)^t[/tex]
b) What is the balance after 1 year? 2 years? 5 years? 10 years?
After 1 year:
[tex]A(1) = 10083(1.068)^{1} = 10,768.644[/tex]
The balance after 1 year is of $10,768.644
After 2 years:
[tex]A(2) = 10083(1.068)^{2} = 11,500.91[/tex]
The balance after 2 years is of $11,500.91.
After 5 years:
[tex]A(5) = 10083(1.068)^{5} = 14,010.25[/tex]
The balance after 5 years is of $14,010.25.
After 10 years:
[tex]A(10) = 10083(1.068)^{10} = 19,467.15[/tex]
The balance after 10 years is of $19,467.15.
c) What is the doubling time?
This is t for which [tex]A(t) = 2A(0)[/tex]. So
[tex]A(t) = A(0)(1.068)^t[/tex]
[tex](1.068)^t = 2[/tex]
[tex]\log{(1.068)^t} = \log{2}[/tex]
[tex]t\log{1.068} = \log{2}[/tex]
[tex]t = \frac{\log{2}}{\log{1.068}}[/tex]
[tex]t = 10.54[/tex]
The doubling time is of 10.54 years.
Sean and Hope are going bowling. For each person, a game costs $4.25. Shoe rentals are $3.00. Sean gives the clerk $20 for their admission and shoe rental. How much change should he receive? *
1 point
$12.75
$5.50
$9.75
$14.50
PLZ HELPPP ME NEED IT BY TODAYYYYYYYYYY!!!!!!!!!!!!!
Answer:
The answer is 5.50.
Step-by-step explanation:
First, you do 4.25+3.00=7.25
Second, 20-7.25=12.75
but read the beggining again it says sean AND hope so repeat the step again.
First, you do 4.25+3.00=7.25
Second, 20-14.50=5.50
giving brainliest *easy*!!
Answer:
254.47
Step-by-step explanation:
254.469
What is the range of the data set?
Answer:
3-15
Step-by-step explanation:
Answer:
12
Step-by-1step explanation:
THE RANGE IS THE BIGGEST NUMBER MINUS THE SMALLEST NUMBER SO 15 - 3 = 12 (sorry for caps lock)
Hope this helps!! Have a great day and don't forget, you are loved.
24 to the second power divided by 47
Answer:
[tex]\frac{576}{47}[/tex]
Step-by-step explanation:
[tex]24^{2} = 576[/tex], since 47 is a prime number and 576 isn't divisible by it, [tex]\frac{576}{47}[/tex] would be the best answer.
1. Find the surface area of the triangular pyramid.
12 yd
17.3 yd
20 yd
What is the surface area of the triangular pyramid
Which of the data sets below has a mean of 32? Select all that apply.
A) 45, 21, 33, 29
B) 18, 54, 24
C) 14, 56, 34, 18, 23
D) 34, 35, 21, 29, 46
Answer:
B is the correct answer
Step-by-step explanation: When you add 18+54+24=96 divide 96 by 3 and its 32!
Use the washer method to find the volume?
It's not clear whether you're talking about the bounded region to the left or right of the y-axis, but due to symmetry it doesn't really matter.
The two curves y = 8 and y = 8x ² intersect for
8 = 8x ² → x ² = 1 → x = -1, x = 1
but we only care about one of these; take the positive solution, so the region of interest lies to the right of the y-axis.
Each washer has an outer radius (distance from the "top" curve to the axis of revolution) of 8 and an inner radius (distance from the "bottom" curve) of 8x ². Take the heights to be some small length ∆x . Then each has a volume of π (outer radius)² - π (inner radius)², or
π (64 - 64x ⁴) ∆x
Now take n such washers, take their sum, and let n → ∞ and ∆x → 0. This amounts to computing the integral,
∫₀¹ π (64 - 64x ⁴) dx = π (64x - 64/5 x ⁵) |₀¹
… = π (64 - 64/5)
… = 256π/5
The two curves y = 8 and y = 8x ² intersect for
8 = 8x ² → x ² = 1 → x = -1, x = 1
but we only care about one of these; take the positive solution, so the region of interest lies to the right of the y-axis.
Each washer has an outer radius (distance from the "top" curve to the axis of revolution) of 8 and an inner radius (distance from the "bottom" curve) of 8x ². Take the heights to be some small length ∆x . Then each has a volume of π (outer radius)² - π (inner radius)², or
π (64 - 64x ⁴) ∆x
Now take n such washers, take their sum, and let n → ∞ and ∆x → 0. This amounts to computing the integral,
∫₀¹ π (64 - 64x ⁴) dx = π (64x - 64/5 x ⁵) |₀¹
… = π (64 - 64/5)
… = 256π/5
THANKS
The following data points represent the number of
patients that were seen by each doctor at Brodin Medical
Center last week.
Sort the data from least to greatest.
4 9
17 7 12
11
5
Find the median number of patients.
The sum of k and 8. what would the expression be?
PLEASE HELP !! ILL GIVE BRAINLIEST *EXTRA 40 POINTS* DONT SKIP :(( .!
Answer: the answer is c
Step-by-step explanation:
Answer:
Angles STQ & RQT
Step-by-step explanation:
They are on opposite sides, but they are also interior.
Hope this helps! Have a good day!
This shape has all identical faces and a surface area of 240 square meters. What is the area of each face?
A 120
B 80
C 60
D 30
Answer: C 60
Step-by-step explanation:
240 is the square meter, and if each face is the same, u divide 240 by 4 which equals 60
please i am struggling allot please
Answer:
The tree grows 3,14 centimeters per year
what is the surface area of the cylinder with the height of 6ft and the radius of 6ft. round your answer to the nearest thousandth.
please NO LINKS!!!
ANSWER THE QUESTION FOR BRAINLIEST
ANSWER THE QUESTION FOR BRAINLIEST
ANSWER THE QUESTION FOR BRAINLIEST
ANSWER THE QUESTION FOR BRAINLIEST
Answer: B
Step-by-step explanation: Hope this help :D
Answer: The answer is B X, 20, 21, 22 and Y, 200, 400, 600
Step-by-step explanation:
I hope this helps have a good and blessed day.
The average prices of a gallon of fuel are shown in the table. Let p=f(t) be the average price of fuel at t years since 1980. The model f(t)=0.0075t2−0.2t+2.32 fits the data well.
Year
Price (dollars per gallon)
1980
2.38
1985
1.57
1990
1.18
1995
0.95
2001
1.33
2005
1.95
2006
2.35
a. Find the p-intercept of the model.
The p-intercept is nothing.
(Type an ordered pair. Type an integer or decimal rounded to two decimal places as needed.)
5−3 when =−2,=4,=6 evaluate
Answer:
x = 2, -1
Step-by-step explanation:
Move all terms to the left side and set equal to zero Then set each factor equal to zero
Is AB tangent to circle C?
Answer:
The line AB is a tangent of the circle with center C.
(Middle school) I’ll give brainliest
Answer:
150.72 units^3
Step-by-step explanation:
Formula: πr2h
3.14 x 4^2 x 3 = 150.72 units^3
Lucas used the number sentence 8 x 2 = 16 to solve a problem. Which problem could he have solved?
Answer:
Word problem 3
Step-by-step explanation:
Word Problem one is a subtraction problem since Felicia is giving away two marbles to Lucas. Word Problem two is a division problem since Felicia is evenly dividing the number of marbles she has into two bags. Word Problem three is a multiplication problem because Ryan has two times as many marbles that Felicia does. Word Problem four is an addition problem because she found two more marbles while she already has eight marbles. Keywords for subtraction word problems are: fewer than, decrease, take away, less than, minus, difference, change, lost reduced, and subtract. Keywords for division word problems are: As much, cut up, groups, equally, sharing, half, how many in each, parts, per percent, quotient, ratio, and separated. Keywords for multiplication word problems are: double, every, factor, increased, multiplied product, times, and tripled.
Need some helps fast like right now
which event is unlikely, but not impossible?
A. spinning a spinner split into a 16 equal sections labeled 1-16 and landing on a 3
HELPPPPPPP PLEASE AND BRAINLY STOP ASKING ME TO WRITE MORE IM IN URGENCY
Answer: 1,431
Step-by-step explanation:
split the thing into two rectangular prisms
small prism dimensions: 18 x 2 x 3
multiply the dimensions to get 108
large prism dimensions: 7 x 21 x 9
multiply the dimensions to get 1,323
add 1,323 and 108 together to get 1,431
can u help pleasee (no links)
The admission prices for a small fair are $1.50 for children and $4.00 for adults. In one day there was $5050 collected. If we know that 2100 children paid admission, find the number of adults that paid admission.
Answer: 475 adults paid admission
Step-by-step explanation:
1.50c+4a=5050 (1.50 per child and 4 per adult)
1.50(2100)+4c=5050 (2100 children times 1.5 each)
3130+4a=5050
4a=1900
a=475
Please solve this
I will mark you as brainleist
I will like your answer
I will give you five stars
I will follow you
Answer: -5
= (-50 + 5)/9
= -45/9
= -5
Answer: -5
Step-by-step explanation:
-50+5= -45
-45/9= -5
nick is baking fudge. what is the minimum amount of plastic wrap needed to cover this piece of fudge?
Answer:
4 inches
Step-by-step explanation:
Answer:
where is the picture?
Step-by-step explanation:
Can someone help me pls I’m stuck
Answer:
Given quadrilateral can't be inscribed in a circle.
Step-by-step explanation:
Property of a cyclic quadrilateral,
Sum of opposite angles of a cyclic quadrilateral is 180°
If the given quadrilateral fulfills this property, it can be inscribed in a circle.
From the given quadrilateral,
Sum of opposite angles = 168° + 22°
= 190°
Therefore, answer is NO.
Given quadrilateral can't be inscribed in a circle.
What is the height, in yards, of a cylindrical water tank that holds 1,884 cubic yards of water and has a diameter of 120 feet? Be sure to convert so you are using like units.
Answer:
The height of the tank is 0.5 yards.
Step-by-step explanation:
To determine what is the height, in yards, of a cylindrical water tank that holds 1,884 cubic yards of water and has a diameter of 120 feet, knowing that the volume of a cylinder is equal to pi multiplied by the radius squared, multiplied by the height, the following calculation must be done:
1 foot = 0.3333 yards
R = Diameter / 2
R = 120/2 = 60
3.14 x 60 ^ 2 x H = 1,884
3.14 x 3,600 x H = 1,884
3.14 x 1,200 x H = 1,884
3.768 x H = 1.884
H = 1,884 / 3,768
H = 0.5
Therefore, the height of the tank is 0.5 yards.
The radius of a circle is 9 feet. What is the circle's area?
HELP! I’ll mark you brainliest! Find the area of the irregular figure.
Answer:
[tex] 177 \: cm^2 [/tex]
Step-by-step explanation:
Area of the irregular figure = Area of rectangle with dimensions 15 cm & 10 cm + Area of rectangle with dimensions (15-6-6=3) 3 cm and 2 cm + Area of triangle with base ( 2 + 2 + 3 = 7) 7 cm and height (18 - 10 - 2 = 6) 6 cm
[tex] = 15 \times 10 + 3 \times 2 + \frac{1}{2} \times 7 \times 6 \\ \\ = 150 + 6 + 21 \\ \\ = 177 \: {cm}^{2} [/tex]
