Ana opened a bank account with $1000 that earns interest, compounded continuously, at an annual rate of r=0.02 . Money can be withdrawn from the account at regular intervals, and no additions to the account can be made. The function P models the balance of the account, in dollars, at time t. Assume that Ana withdraws money from the account continuously at a rate of N dollars per year.

Required:
Write down the differential equations that best describes the relationship between P and t?

Answers

Answer 1

Answer:

dp/dt = 0.02P-N

Step-by-step explanation:

[tex]\frac{p(t+t)}{nt}[/tex]

Answer 2

The differential equation that describes the relationship between P and t is:

dP/dt = rP - N

where P is the balance in dollars, t is time in years, r is the annual interest rate, and N is the rate of withdrawals in dollars per year.

What is a differential equation ?

A differential equation is an equation that relates an unknown function to its derivatives (or differentials) with respect to one or more independent variables. In other words, it is an equation that involves derivatives of an unknown function.

The rate of change of the balance P in the bank account is equal to the difference between the rate of interest earned on the account and the rate at which money is withdrawn from the account.

The rate of interest earned on the account is given by the continuous compounding formula:

dP/dt = rP

where r is the annual interest rate, P is the balance in dollars, and dP/dt is the rate of change of P with respect to time.

On the other hand, the rate at which money is withdrawn from the account is given by the expression:

dN/dt = N/T

where N is the rate of withdrawals in dollars per year, and T is the time interval in years between withdrawals.

If we assume that Ana withdraws money from the account continuously at a rate of N dollars per year, we can write:

N = dN/dt

Substituting this into the first equation, we get:

dP/dt = rP - dN/dt

Substituting the expression for dN/dt, we get:

dP/dt = rP - N/T

Simplifying, we get:

dP/dt = rP - N

which is the differential equation that describes the relationship between P and t.

The differential equation

dP/dt = rP - N

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Related Questions

find the area of the triangle ​

Answers

Answer:

133

Step-by-step explanation:

14 times 19 is 266 divided by 2 is 133

Area of a triangle is 1/2 x base x height

Base is given as 19 ft and height is given as 14 ft

Area = 1/2 x 19 x 14 = 133 square ft


Shidjdjzjzjzjzjzjzjzjzjzjzzjzjzjzjzjzj

Answers

Answer:

14130 yd³

Step-by-step explanation:

The formula of volume of sphere

[tex] = \frac{4}{3} \pi {r}^{3}[/tex]

The volume of the sphere

[tex] = \frac{4}{3} \times 3.14 \times {(30 \div 2)}^{3} [/tex]

[tex] = \frac{4}{3} \times 3.14 \times {15}^{3} [/tex]

[tex] = \frac{42390}{3} [/tex]

= 14130 yd³

4x+2y=16
3x+4y=17
i need help

Answers

Answer:

x = 3 , y = 2

Step-by-step explanation:

Nancy uses her $10 allowance to buy a dress. She got $2 bills and 2quarters in change. what was the price of the dress???

Answers

Answer:cdjbskbbN

Step-by-step explanation:2 2/4

Answer:

$7.50

Step-by-step explanation:

10 - 2.50 = 7.50

3.
A man has 6 packages. Their average weight is 18 kg. Find the total
weight of the 6 packages.

Answers

Answer:

108 kg for all 6 packages

Step-by-step explanation:

Answer:

=108

Step-by-step explanation:

18 × 6 will give you 108

1 point
Every five years in March, the population of a certain town is recorded. In
1995, the town had a population of 4500 people. From 1995 to 2000, the
population increased by 15%. From 2000 to 2005, the population
decreased by 4%. What was the town's population in 2005? *
4527
4968
4995
5382

Answers

Answer:

So, the town had a population on 4,500 people in 1995. Then from 1995 to 2000, the population increased by 15%.

Convert 15% to a decimal by dividing it by 100. Then, the population in 1995 by this decimal.

15% ÷ 100 = 0.15

4,500 × 0.15 = 675

Now, add this to the population in 1995.

4,500 + 675 = 5,175

This means that the town had a population of 5,175 people in 2000.

To calculate the town's population in 2005, repeat the same steps we took to find the population in 2000, except this time we will subtract instead of add since the population DECREASED.

4% ÷ 100 = 0.4

5,175 × 0.4 = 207

5,175 - 207 = 4,968

FINAL ANSWER:

The town had a population of 4,968 in 2005.

Click to let others know, how helpful is it

0.0

0 votes

  Report

Step-by-step explanation:

look at pic 10 pts will mark brainilest

Answers

Answer:

1,400

Step-by-step explanation:

Evaluate for x=2

100(2^3+2^2+2)

=1400

PLZ give me brainliest

Can someone help me with this, please!!!

Answers

Answer:

The answer is C

Step-by-step explanation:

Both triangles are very similar

what is the unit price of 12 cupcakes for 25 dollars​

Answers

Answer:

Unit price of 12 cupcakes for 25 dollars = 25/12

= 2.08 dollars

Answer:

The unit price would be $2.08 for a cupcake because if you divide 12 and 25, you would get 2.08.

Step-by-step explanation:

What is a decimal that is equivalent to the fraction 44/100​

Answers

Answer:

0.44

Step-by-step explanation:

44/100 as a decimal is 0.44.

Hope this helped!!!

The decimal equivalent to the fraction 44/100 is 0.44.

We have,

To find a decimal equivalent to the fraction 44/100, we can simply divide the numerator (44) by the denominator (100):

44 ÷ 100 = 0.44

The concept used to find the decimal equivalent of a fraction is division.

By dividing the numerator by the denominator, we obtain the decimal representation of the fraction.

Therefore,

The decimal equivalent to the fraction 44/100 is 0.44.

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Gino wants to leave at least 20% tip on his restaurant bill of $197.40. Approximately how much tip should he add to the bill?

Answers

So exactly it would be 39.48, but do you want me to round to a specific ten?

name the quadrant in which the point (7,-10) is located PLEASE HELP I NEED IT NOW PLS

Answers

Step-by-step explanation:

the point (7,-10) is located in 1 at quadrant

Answer:

Quadrant 4

Step-by-step explanation:

To find this out, simply get a coordinate plane and plot the coordinate point.

OR

You can remember this formula for coordinate points:

Quadrant 1: (x,y)

Quadrant 2: (-x,y)

Quadrant 3: (-x,-y)

Quadrant 4: (x,-y)

Point (7,-10) has a positive x-coordinate and a negative y-coordinate. This means it belongs in quadrant 4.

You are buying shoes online. The selling price is $29.99. The sales tax is 6.5% What is the total cost? Round to the nearest penny, if necessary.

Answers

Answer:

$31.94

Step-by-step explanation:

29.99 x 0.065 = 1.95

29.99 + 1.95= 31.94 :)

Answer:

$31.94

Step-by-step explanation:

What is the probability of choosing a king from a deck of cards? Type your answer as a fraction.

Answers

Answer:

4/52 or 1/13

Step-by-step explanation:

there are only 4 kings; diamond, Heart, Spades and Clubs.

4/52 because there is one king for every suit and only 4 kings total in the deck of 52!

maths question solve it quick pls​

Answers

Answer:

(a)2 1/4

(b)1 1/2

(c)1 1/18

(d)5 7/12

Step-by-step explanation:

(a) 11/3 - 17/12 = 44/12 - 17/12 = 27/12 = 9/4 = 2 1/4

(b) 33/10 - 18/10 = 15/10 = 3/2 = 1 1/2

(c) 41/9 - 7/2 = 82/18 - 63/18 = 19/18 = 1 1/18

(d) 47/6 - 9/4 = 94/12 - 27/12 = 67/12 = 5 7/12

Hope it helped :)

a) 3 2/3 - 1 5/12 we’ll convert to 12ths by multiplying the numerator and denominator of the first mixed number by 4.
3 8/12 - 1 5/12 = 2 3/12 = 2 1/4

b) 3 3/10 - 1 4/5 we’ll convert to 10ths by multiplying the numerator and denominator of the second mixed number by two.

3 3/10 - 1 8/10
Now we need to borrow from the three wholes to create more tenths
2 13/10 - 1 8/10 = 1 5/10 = 1 1/2

Or you can convert the first one to 33/10, and the second one to 9/5, which becomes 18/10.
33/10 - 18/10 = 15/10 = 1 1/2
Do whichever one makes more sense to your brain.

c) 4 5/9 - 3 1/2 we will convert both to 18ths.
4 10/18 - 3 9/18 = 1 1/18

d) 7 5/6 - 2 1/4 we will convert both to 12ths.
7 10/12 - 2 3/12 = 5 7/12

Please let me know if you have questions on these.

A baker uses a circular pan with a 24-inch diameter to make a pizza. What is the area of the pizza? Round to the nearest hundredths


A. 37.68
B. 75.36
C. 1808.64
D. 452.16

Answers

Answer:

D

Step-by-step explanation:

A = πr^2

A = π12^2

A = π144

A ≈ 452.16

Answer:

The answer is 452.16

Step-by-step explanation:

If you don't believe me you can use a circle calculator

Express the relation in a table:(2,1),(4,5),(3,3),(1,(2)

Answers

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

Once the data is entered into a spreadsheet, it is convenient to sort the table by the input values. The relation is unchanged, but it may be easier to work with that way.

The table is shown below.

What is the solution to this equation? 3v(1/8-x)=-1/2

Answers

Answer:

v = −4/−24x+3

Step-by-step explanation:

Let's solve for v.

3v(1/8−x) = −1/2

Step 1: Factor out variable v.

v(−24x+3/8) = −1/2

Step 2: Divide both sides by (-24x+3)/8.

v(−24x+3/8)/−24x+3/8 = −1/2/−24x+3/8

v=−4/−24x+3

Write down the integer values satisfied by the diagram

Answers

Answer:

{0, 1, 2, 3}

Step-by-step explanation:

The diagram includes the interval:

(-1, 3]

The integer values in the given interval are:

{0, 1, 2, 3}

What would y be if x was equal to 410 billion?

Answers

It could be any number

Answer:

it would be any number because variables don't mean a certain,number

Can someone explain me this

Answers

Answer:

area of circle - area of hexagon

Step-by-step explanation:

Allen has a piece of wood that is 10.5 feet long. He decides to cut it into 3 equal pieces to repair his deck. How long should he cut each piece?

Answers

Answer:

3.5 feet

I think is right

Find the point on a circle that has a radius of 8 with an angle of rotation of 130 degrees centered at (-3,5)?

Answers

-2,8
Is it
Jusmfjfkddnfnfnfnjdf just to let me post :)

Please help me with this ASAP ASAP please please help

Answers

Answer:

4ㅈr² is formula

so

4 × ㅈ× (16)²

= 1024ㅈ cm²

Can someone solve this?

Answers

Answer:

The answer is A.

Step-by-step explanation:

Because if you compare the two "y" section on both graphs you will notice that the "Speedy Delivery" charges way more than the "Lightning Delivery ."

Hope this helps ,have a good day.

What is the value of x?

Answers

Answer:

x = 21

Step-by-step explanation:

The two angles shown are supplementary.

3x + 10 + 6x - 19 = 180

9x - 9 = 180

9x = 189

x = 21

The figure is a ____.

1. Square

2. Rectangle

3. Triangle

The figure has _____ sides.

1. Three

2. Four

3. Five

The figure has the dimensions of _____.

1. Length, Width, and height

2. Length, Width, Base, and height

3. Length and Width

(also ignore my mouse)

Answers

The figure is a rectangle.

The figure has Four sides.

The figure has the dimensions of Length and Width.

Sorry if its wrong, I have bad memory

1. Rectangle
2. Four
3. Length, width, and height

Make frequency tables for the following data sets. Include columns for relative frequency. Also, make a bar graph for the frequency
Final grades of 30 students in a math class: AAAAAABBBBBBCCCCCCCCCCFFF

Answers

It’s 4 because I think so

The ratio of children to adults is 4 to 3. How many children are there if there are 2700 adults?

Answers

Answer:

2025 children

Step-by-step explanation:

4 2700

-- = --------

3 x

cross multiply

4x = 8100

x = 2025

Installment Loan
Principal
$1500.00
Term Length
4 years
How much of the first
payment for the
installment loan
6% shown in the table will
go towards interest?
Interest Rate
Monthly Payment
$35.00
A. $27.50
B. $7.50
C. $2.10
D. $32.90

Answers

The amount of the first payment that will go towards interest is $7.50.

The answer is B. $7.50.

To calculate the amount of the first payment that will go towards interest for an installment loan, we need to consider the principal, term length, and interest rate.

Given:

Principal: $1500.00

Term Length: 4 years

Interest Rate: 6%

Monthly Payment: $35.00

To find the amount of interest paid in the first payment, we'll first calculate the total interest paid over the entire term and then divide it by the number of payments.

Calculate the total interest paid over the term.

Total Interest = Principal × Interest Rate × Term Length

Total Interest = $1500.00 × 6% × 4 = $360.00

Divide the total interest by the number of payments.

Interest in the First Payment = Total Interest / Number of Payments

Interest in the First Payment = $360.00 / (4 years × 12 months per year)

Interest in the First Payment = $360.00 / 48

Interest in the First Payment = $7.50

Therefore, the amount of the first payment that will go towards interest is $7.50.

The answer is B. $7.50.

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