Answer:
It will take 14 years before the investment triples
Step-by-step explanation:
Continuous Compounding
Is the mathematical limit that compound interest can reach if it was calculated and reinvested into an account's balance over a theoretically infinite number of periods.
The formula for continuous compounding is derived from the formula for the future value of a compound interest investment:
[tex]FV = PV\cdot e^{i.t}[/tex]
Where:
FV = Future value of the investment
PV = Present value of the investment
i = Interest rate
t = Time
It's required to find the time for an investment to triple, that is, FV = 3 PV, knowing the interest rate is i=8%=0.08.
Substituting the known values:
[tex]3PV = PV\cdot e^{i.t}[/tex]
Dividing by PV:
[tex]3 = e^{i.t}[/tex]
Taking logarithms:
[tex]\ln 3=i.t[/tex]
Solving for t:
[tex]\displaystyle t=\frac{\ln 3}{i}[/tex]
[tex]\displaystyle t=\frac{\ln 3}{0.08}[/tex]
t = 13.7 years
Rounding up:
It will take 14 years before the investment triples
It will take 37.5 years before the investment triples.
The formula for calculating the future value is expressed as:
[tex]A =Pe^{rt}[/tex]
P is the principal
r is the rate (in %)
t is the time (in years)
If the investment tripled, then A = 3P. The equation will become:
[tex]3P=Pe^{rt}\\3=e^{rt}\\ln3 =lne^{rt}\\rt = 3\\0.08t =3\\t =\frac{3}{0.08} \\t =37.5 years[/tex]
Hence it will take 37.5 years before the investment triples.
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Beth deposited $ 4,000 in a collage fund earning 3.5 % simple interest.
what was the total interest earned at the end of 12 years.
Answer:
140 total interest
Step-by-step explanation:
What is the slope of the line that passes through the points (-3,-9) and (22,-4)
Answer: 1/5
Step-by-step explanation:
Write the slope-intercept form of the equation of the line.
slope = -5, y - int = -3
Answer:
y= -5x-3
Step-by-step explanation: Hope this helped!!!
btw can i have brainliest?
solve 58×29 using a area model
Answer:
1,682
Step-by-step explanation:
Answer:
1,682
Step-by-step explanation:
Use the sliders to change the values of a, b, c, and d in the cosine function. Which equation has a maximum at (0, –1) and a minimum at ((StartFraction pi Over 3, negative 5)).
Answer:
If you have to do the sliders problem the answeres in order are, set a to -3, set b to 2 and keep c at 0.
Step-by-step explanation:
the correct answer is y=-3 sin(2x) and the equation from the sliders should match the answer.
y=-3 sin(2x) is the equation has a maximum at (0, –1) and a minimum at ( pi Over 3, negative 5)
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Given,
We need to use the sliders to change the values of a, b, c, and d in the cosine function.
We need to find the equation which has maximum at (0, –1) and a minimum at (pi Over 3, negative 5)).
While doing slider problems we have to set the values as set a to -3, set b to 2 and keep c at 0.
y=-3 sin(2x) is the answer and the equation from the sliders should match the answer.
Hence y=-3 sin(2x) is the equation has a maximum at (0, –1) and a minimum at ( pi Over 3, negative 5)
To learn more on trigonometry click:
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In a circle, what is the ratio of the circumference to its diameter?
area
radius
volume
PI
Answer:
D. pi
Step-by-step explanation:
Circumference of a circle = [tex] \pi d [/tex]
Diameter = d
Therefore, ratio of circumference of a circle to its diameter would be:
[tex] \pi d : d [/tex]
[tex] = \frac{\pi d}{d} = \pi [/tex] => (d cancels d)
Therefore, the ratio of the circumference of a circle to its diameter is [tex] \pi [/tex]
A transportation agency has one 38-seater bus and some 13-seater buses. They have enough seats to board no more than 417 passengers on
their buses. Which inequality represents the possible number of 18-seater buses they have.
Ov12
Answer:
24
Step-by-step explanation:
start at 4. create a pattern that multiplies each number by 4 and then adds 3. when you have 5 numbers
Answer:
4,19,79,320,1284
Step-by-step explanation:
Can anyone answer this please?
Answer:
5
Step-by-step explanation:
just look at the graph
HELP! ASAP!
Select all the expressions with a value of less than one.
Answer: all but the first one because anything to the power of 0 is one and -1 is lower than 1
Answer:
B, C, D, E
Step-by-step explanation:
N+3(n-1) i need helpppp
Answer:
4n - 3
Step-by-step explanation:
N + 3 (n - 1)
N + 3n - 3
4n - 3 is the final answer
hope that helps :))
A rectangular building with a square front is to be constructed of materials that costs 11 dollars per ft2 for the flat roof, 14 dollars per ft2 for the sides and the back, and 15 dollars per ft2 for the glass front. We will ignore the bottom of the building. If the volume of the building is 5,600 ft3, what dimensions will minimize the cost of materials? (Round your answers to the nearest hundreth such that the dimensions increase from the smallest to the largest.)
Answer:
y = 23.14 ft
x = 15.56 ft
so the dimensions of the building will be = 15.56 ft x 15.56 ft x 23.14 ft
Step-by-step explanation:
the area of the roof = xy
cost of the roof = 11xy
the area of the sides and back = 2xy + x²
cost of the sides and back = 14(2xy + x²) = 28xy + 14x²
area of the glass front = x²
cost of the glass front = 15x²
minimize:
total cost = 11xy + 28xy + 14x² + 15x² = 39xy + 29x²
total volume = x²y = 5600 ⇒ constraint
39y + 58x = 2λxy
39x = λx2
x²y = 5600
λx = 39 which we replace into the first equation
39y + 58x = 78y
58x = 39y
(58x)²y = 58² · 5600
now we replace 58x by 39y
(39y)²y = 58² · 5600
39² · y³ = 58² · 5600
y³ = (58² · 5600) / 39² = 12,385.53583
y = ∛12,385.53583 = 23.14 ft
x² = 5600/ 23.14 = 242.04
x = 15.56 ft
Find the temperature indicated on this thermometer.
Answer:
55 degrees
Step-by-step explanation:
always the middle of the thermometer is 15,25,35,45,55,65,75,85,95 etc.
7. Write the slope-intercept form of the equation of the line.
slope = -5 , y - int = -1
Answer:
Y=-1/5x-1
Step-by-step explanation:
Combine the slope then the slope intercept.
What is the area of the right triangle below?
Answer: The answer is a 25 square units
Step-by-step explanation:
4. An isosceles triangle has sides that measure 7cm and 15cm. Find the third side of the
triangle, then find the perimeter.
Answer:
Third side is 15cm. Perimeter is 37cm.
Step-by-step explanation:
In a triangle sum of two sides is always greater than third side. Two sides of a isosceles triangle are equal.
So if the third side is 7cm
7+7=14cm which is less than 15 cm.
hence third side is 15 cm as
15+15=30cm which is greater than 7cm
15+7=22cm which is greater than 12cm
then
perimeter=15+7+15=37cm
Solve the equation for x do not include "x=" in your answer -2+/3x-2=6
Answer:
x=1=2y
Step-by-step explanation:
If Pam has 30 dollars in her account, how much money does her brother have in his account if the total is $100? Use a tape diagram to support your answer.
There is 1/3 of a pizza left to split between 3 of your friends. If you split the pizza equally what fraction of the pizza will each s get
Answer:
1/9
Step-by-step explanation:
Which sampling method was used?
A.
B.
C.
D.
2.x2-9x + 18
А. x-2
В. Х-3
С. x+2
D. x+ 3
5% of items in a large batch of items produced at a local foundry' are defective. If 50 of these items are selected at random, what is the probability that exactly 2 of the items will be defective? Round to four decimal places.
Answer:
0.2611
Step-by-step explanation:
We have x to be binomially distributed random variable which denotes the items number that are defective
We have been given n = 59 as our sample size
Probability of 5% = probability of success
1-5% = 0.95
We solve using this formula
nCxP^xq^n-x
= 50C2(0.05)²(0.95)^50-2
= 0.2611
This is the probability that exactly 2 would be defective
I just need number 1
b is the awnser
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
There are 96 squares in total. Yard is 3 feet, so you would divide the total by 3.
I need help. Thanks in advance
Answer:
6u²−3uv²−4u⁴+5uv
Step-by-step explanation:
i had a test with this and got it right
Write the slope-intercept form of the equation of the line.
slope = 0, y - int=1
Answer:
y= 1
Step-by-step explanation:
This is because there will be no increase or decrease of x since we have no slope to take us there so it will remain constant at the y value
Hope This Helps :)
Answer:
The answer is there. Look it up.
Step-by-step explanation:
which integer represents each situation
deposit of $15
Answer: +15
Step-by-step explanation: A deposit of $15 is an increase,
which means that it's positive.
So it can be written as +15.
Devaughn is 7 years older than Sydney. The sum of their ages is 89. What is Sydney's age?
Answer: 82
Step-by-step explanation:
Solve the
equation:
-22 + x = 11
Answer:
[tex]x=33[/tex]
Step-by-step explanation:
Add 22 to both sides of the equation.
[tex]x=11+22[/tex]
Add 11 and 22.
[tex]x=33[/tex]
Answer:
x=33
Step-by-step explanation
Regroup terms.
x−22=11
Add 22 to both sides.
x=11+22
Simplify 11+22 to 33
ANDDDD the answer isss
x=33
what the awnser 2/4 x 4/8
Answer: 1/4 or 0.25.
Step-by-step explanation: 2/4 x 4/8 = 8/32 = 1/4 = 0.25.
Answer:
1/4 or 0.25
Step-by-step explanation:
2/4 * 4/8 =
2*4=8 and 4*8=32
so 2/4 * 4/8 = 8/32
8/32 = 1/4 = 0.25
So the answer is:
1/4 or 0.25
What is −15 ÷ 3/5?
−25
−9
−19
−125
Answer:
-25, or a
Step-by-step explanation: