Tyler invested $350 in an account paying an interest rate of 4.5% compounded
continuously. Assuming no deposits or withdrawals are made, how long would it
take, to the nearest tenth of a year, for the value of the account to reach $700?
Answers
Answer:
15.4 I did this on delta math
It would take approximately 15.4 years, to the nearest tenth of a year, for the value of the account to reach $700 with continuous compounding.
How to calculate compounding time?The formula for calculating the future value (FV) of an investment with continuous compounding is:
[tex]FV = Pe^{rt}[/tex]
Where P is the initial principal, r is the annual interest rate (expressed as a decimal), t is the time period (in years), and e is the mathematical constant e (approximately 2.71828).
In this case, we have P = $350, r = 4.5% = 0.045, and we want to find the time t when the FV is $700. Substituting these values into the formula, we get:
[tex]700 = 350e^{0.045t}[/tex]
Dividing both sides by $350, we get:
[tex]2 = e^{0.045t}[/tex]
Taking the natural logarithm of both sides, we get:
[tex]ln(2) = ln\times e^{0.045t}[/tex]
Using the properties of logarithms, we can simplify this to:
ln(2) = 0.045t ln(e)
Since ln(e) = 1, we can simplify further to:
ln(2) = 0.045t
Finally, solving for t, we get:
t = ln(2) / 0.045 ≈ 15.4
Therefore, it would take approximately 15.4 years, to the nearest tenth of a year, for the value of the account to reach $700 with continuous compounding.
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Related Questions
Can some one plz help me
Answers
Answer:
Step-by-step explanation:
A is midpoint of DB
DA ≅ AB ------------------(I)
B is midpoint of AE
BE≅ AB ---------------(II)
From (I) & (II)
DA ≅ AB
∠D ≅ ∠E Given
CD ≅ CE {Sides opposite to equal angles are equal}
ΔCDA ≅ ΔCEB { S A S congruent}
Answer:
AB = BA reflexive property
AB = BE and DA = AB definition of midpoint
then DA = EB
CD = CE ΔCDE is isosceles
ΔCDA ≅ ΔCEB SAS
Step-by-step explanation:
Please help me.. I’m not really good at math so please??
Answers
Witch answer choice represents a person running 90 calories by climbing 18 flights of stairs
Answers
Answer:
fr
Step-by-step explanation:
fr
There are 640 calories in 4 scoops of ice cream. At this rate, how many calories would there be in 9 scoops of ice cream?
Answers
Answer:
1,440 calories
Step-by-step explanation:
Divide 640 by 4 to get how many calories there are per scoop.
640 calories ÷ 4 scoops = 160 calories per scoop
Then, we can multiple 160 by 9 to get the calories in 9 scoops.
160 calories per scoop × 9 scoops = 1,440 calories per 9 scoops
Answer:
1,440
Step-by-step explanation:
What is the distance from -7 to 5 on a number line?
2
4
-12
12
Answers
Answer:
12 units
Step-by-step explanation:
Find the absolute value of the difference , that is
d = | - 7 - 5 | = | - 12 | = 12 or
d = | 5 - (- 7) | = | 5 + 7 | = | 12 | = 12
The distance from -7 to 5 on a number line is 12 units. This distance between two integers is calculated by using a number line and the absolute value of the difference between those two integers.
What is a Number line?A number line is a graph for the real numbers.It is used to represent the integers on it at a regular interval. It is also used for finding arithmetic operations like the addition and subtraction of integers.The positive integers lie on the right side of the number line and the negative integers lie on the left side of the line The zero lies at the center of the line which separates the positive and negative integers.How to calculate the distance between two integers on a number line?For calculating the distance between two integers, count every integer in between themA faster way of finding the distance between the two integers is by taking the absolute value of their differenceIf A and B are two integers, then the distance between them is given by |B - A|Calculating the distance from -7 to 5 on the number line:
⇒ | 5 - (-7) |
⇒ | 12 |
= 12 units
Therefore, there are 12 units in between the given two integers -7 and 5 on a number line which is shown below
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The function y = f(x) is graphed below. Plot a line segment connecting the points
on f where x = -5 and x = 1. Use the line segment to determine the average rate
of change of the function f(x) on the interval –5 < x < 1?
Answers
Answer:
no not really
Step-by-step explanation:
the values dont match up
Can someone help me with this please
Answers
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
Check out this rectangular prism: Find the surface area of the rectangular prism (above) using its net (below).
Answers
Answer:
Please tell me more
Step-by-step explanation:
Johnny starts run at the 2 mile mark and runs 4 miles per hour. Javier starts at the 6 mile mark and runs 2 miles per hour. How long until Johnny catches up with Javier?
Answers
Answer:
2 hours
Step-by-step explanation:
If the surface area of a cube is 384 square inches, what is the length of each side
Answers
Answer:
There are six equal surfaces of a cube. Then,
384 / 6 = 64 sq in (the area of one surface)
The area of one surface of a cube will be equal to x*x (if we let the edge length be x)
x^2 = 64
x = 8 inch
Step-by-step explanation:
I know i already answered it i just want to make sure im right can someone double check it for me! Sorry
Answers
Answer:
You are correct!!! (<5 and <4 , <3 and <6)
Step-by-step explanation:
5 and 6 are on the same line so they are not alternate and angle 1 is on the outside.
11) Nick & John ordered burritos & tacos for lunch. Nick
ordered 3 burritos & 4 tacos for $11.33. John ordered 9
burritos & 5 tacos for $23.56. Find the cost of one
burrito & one taco.
Answers
Answer:
taco: $1.49 each
burrito: $1.79 each
Step-by-step explanation:
Let b = cost of one burrito
t = cost of one taco
(1) 3b + 4t = 11.33 (2) 9b + 5t = 23.56
Multiply (1) by -3 and add to (2) -9b - 12t = 33.99
- 7t = - 10.43
t = 1.49
3b + 4(1.49) = 11.33
3b + 5.96 = 11.33
3b = 5.37
b = 1.79
What is the volume of the cone? Estimate using 3.14 for pi, and round to the nearest tenth
Answers
Answer:
V=πr2h3
r Radius
h Height
Right circular cone
Answer:
its going to be 21 or 20 I think I'm not sure
A rectangular prism is shown below. Find the volume. 1.3 ft 1.5 ft 2.3 ft 23 “ Your answer can be exact or rounded to the nearest tenth.
Answers
Answer:
4.485 ( rounded = 4.5)
Step-by-step explanation:
1.3 x 1.5 x 2.3 = 4.485
Find the slope of the line
Answers
Answer:
Your answe is 1
Step-by-step explanation:
Formula : y2-y1/x2-x1
the slope is 1
Given two solutions x=-5 and x=7 of a quadratic function, is the value of a =1 or can the value of a different value?
Answers
I always get these mixed up, can someone help me?
Answers
Answer:
The answer is
1_ side angle side
2_angle side angle
3_ angle angle side
4_ side side side
lilly rents a bike for $15 plus $2 per hour. What algeraic expression represents the situation?
Answers
Answer:
Solution
Step-by-step explanation:
If im wrong let me know okay!
If im wrong Im sorry Im only 15 and im working here to help
Answer:
$15 + $2 = h
Step-by-step explanation:
( h = per hour) lilly rents a bike for $15 plus $2 per hour,
Please help!!!! I need it
Answers
Answer:
Look to explanation for help with answer :)
Step-by-step explanation:
Each year 50 new bulbs are added, so the gardener can expect that many added plants each year. So add 50 6 times and that will get to how many new bulbs will be added by 10 years time. More and more plants will be added each year and depending on which method the gardener chooses to use it will affect the buying amounts for each year as well as how many are bought.
I hope this helps! Good luck!
And the second question asks
Are the systems of equations
equivalent?
Yes
No
Answers
work out the equation of the line which has a gradient of 2 and passes through the point (1, 4)
Answers
Answer:
y = 2x + 2
Step-by-step explanation:
The slope is also called the gradient of the line.
The slope that is given is two, and the point is (1, 4).
I made a point slope equation, and then converted it into a slope-intercept equation.
[tex]y-4=2(x-1)\\\\y-4=2x-2\\\\y-4+4=2x-2+4\\\\\boxed{y=2x+2}[/tex]
Hope this helps.
the question is on the picture :)
Answers
Answer:
2.5
Step-by-step explanation:
y=kx, k is constant of prop
i bought a box of air head worth $7.98 there are 60 bars in the box, how much is 1 air head worth? please help
Answers
Answer:
$0.13
Step-by-step explanation:
7.98/60 = 0.133
round down to 0.13
Answer:
I believe the answer is $0.13
Step-by-step explanation:
You need to divide the price of the air heads ($7.98) by how many bars there were in the box (60). 7.98/60= 0.133
Then you round the answer to the nearest hundredth: 0.133= $0.13
Emily walked around 2 parks. One measures 54 feet by 38 feet and other measure 32 feet by 22 feet. How much did she walk?
Answers
Answer:
292 feet
Step-by-step explanation:
If Emily walked round the two rectangular parks, she walked round the perimeter of the parks.
the total distance she walked can be determined by calculating the perimeter of each of the park and adding the perimeters together
Perimeter of a rectangle = 2 x ( length + breadth)
Perimeter of the first park = 2 x (54 ft + 38 ft) = 184 ft
Perimeter of the second park = 2x (32 + 22) = 108 ft
Sum of the perimeters = 184 ft + 108 ft = 292 ft
Mrs. Smith and her two sons spent a total of $53.50 at the movie theater. Together they spent $26.75 on snacks and Mrs. Smith's ticket was $11.25. How much did each son's ticket cost?
Answers
Answer:
$7.75
Step-by-step explanation:
$26.75 + $11.25=$38
$53.50 - $38=$15.5
$15.5/2= $7.75
please help me im giving you a lot of points
Answers
Answer:
7w13 times4y2
Step-by-step explanation:
Help please!?!?!?!?!?!?!?!?!
Answers
Answer:
Your answer is D.
Step-by-step explanation:
If you need explanation ask me in comment
What is the probability of rolling a multiple of 2 with one toss of a number cube?
Answers
Answer:
P(number of cube) = 3/6
=1/2
A triangle has sides with lengths of 44 meters, 55 meters, and 77 meters. Is it a right triangle?
Answers
Answer:
no it is not a right triangle because the lengths add up to 176 and a right triangle should add up to 190.
Step-by-step explanation:
The side measures of the triangle does not form a right triangle.
What is a triangle?A triangle is a flat geometric figure that has three sides and three angles. The sum of the interior angles of a triangle is equal to 180°. The exterior angles sum up to 360°.
For the given situation,
The side lengths of the triangle are 44 meters, 55 meters, 77 meters.
For the triangle to be a right triangle, one interior angle should be 90°.
Based on the sides, by Pythagoras theorem,
Square of long side = sum of square of other two sides
⇒ [tex]77^{2}=44^{2} +55^{2}[/tex]
⇒ [tex]5929=1936+3025[/tex]
⇒ [tex]5929\neq 4961[/tex]
Hence we can conclude that the side measures of the triangle does not form a right triangle.
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Hometown Gym charges a $200 membership fee and $45 per month. Local Gym charges a $50 membership fee and $55 per month. Write an equation to represent the situation. After how many months will the total amount of money paid to both gyms be the same?
Answers
Answer:
=> membership fee = $50
=> monthly fee = $55
=> First month = 105$
=> 50 + 55(x)
=> 50 + 55 (15)
=> 50 + 825
=> 875
Workout gym
=> membership fee = $200
=> monthly fee = $45
=> First month = 245$
=> 200 + 45(x)
=> 200 + 45(15)
=> 200 + 675
=> 875