1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Tomtit [17]
3 years ago
5

A person borrows $10,000 and repays the loan at the rate of $2,400 per year. The lender charges interest of 10% per year. Assumi

ng the payments are made continuously and interest is compounded continuously (a pretty good approximation to reality for long-term loans), the amount M(t) of money (in dollars) owed t years after the loan is made satisfies the differential equationdMdt = 110 M − 2400and the initial conditionM(0) = 10000.(a) Solve this initial-value problem for M(t).M(t) = (b) How long does it take to pay off the loan? That is, at what time t is M(t) = 0? Give your answer (in years) in decimal form with at least 3 decimal digits. years
Mathematics
1 answer:
omeli [17]3 years ago
8 0

Answer:

a) M(t)=24000-14000e^{t/10}

b) It takes 5.390 years to pay off the loan.

Step-by-step explanation:

(a) The differential equation for the variation in the amount of the loan M is

\frac{dM}{dt}=0.1M-2400

We can express this equation as:

\frac{dM}{dt}=0.1M-2400\\\\10\int \frac{dM}{M-24000} =\int dt\\\\10ln(M-24000)=t\\\\M-24000=Ce^{t/10}\\\\M=Ce^{t/10}+24000\\\\M(0)=Ce^{0/10}+24000=10000\\\\C+24000=10000\\\\C=-14000\\\\M(t)=24000-14000e^{t/10}

(b) We can calculate this as M(t)=0

M(t)=24000-14000e^{t/10}=0\\\\e^{t/10}=24000/14000=1.714\\\\t=10ln(1.714)=10* 0.5390=5.390

It takes 5.390 years to pay off the loan.

You might be interested in
The quotient of two less than a number and five is eight
postnew [5]

Answer:

The number is 42.

Step-by-step explanation:

Let x be the unknown number.

"two less than a number" is x - 2

Quotient means the result of a division.

(x - 2)/5 = 8

Multiply both sides by 5.

x - 2 = 40

Add 2 to both sides.

x = 42

Answer: The number is 42.

Check.

Start with 42. 2 less than 42 is 40. The quotient of 40 and 5 is 40/5 which is 8. The answer is correct.

5 0
3 years ago
Is 16x2 - 16x + 4 a perfect square?
Andrew [12]

Answer:

Yes

Step-by-step explanation:

Use the completing the square method:

16(x^2-x)+4

=16((x-1/2)^2 - (1/2)^2)+4

=16((x-1/2)^2 - 1/4)+4

=16((x-1/2)^2) - 16/4 + 4

=16(x-1/2)^2

=4^2(x-1/2)^2

The product of two square is itself a square.

5 0
3 years ago
13. The initial value of a particular vehicle is $20,000. After one year, the vehicle is worth $17,000. If the
Dima020 [189]
I think it would be D that’s what I think
7 0
3 years ago
Using the numbers 8,6,4 and 2 write an expression that equals 4
vfiekz [6]
8-(6+2)+4 is how you use those numbers to equal 4
5 0
3 years ago
Read 2 more answers
What was the property of equality
loris [4]

Reflexive Property=For all real number X,X=X

A number equals itself

Addition Property=For all real number X,y & Z,. if

X=Y then X+y=y+Z

Subtraction Property=For all real number X,Y And Z if X=y then X-Z=y-Z.

7 0
3 years ago
Other questions:
  • Select all ordered pairs that satisfy the function y = 4x + 3
    13·1 answer
  • The Eagle Club wants to build a chain of 2,505 dominoes. If they have already set up 807 dominoes, how many more do they need to
    11·2 answers
  • Jayne says that 0.45 is equal to 4/10 is she correct? Explain
    10·2 answers
  • Write an equation of a line in slope intercept form that contains the points (4,-4) and (-2,-2)
    15·1 answer
  • Which value makes the inequality r > 2.5 TRUE?
    6·1 answer
  • Andy had some basketball cards. After he bought 12 more, he had 48 cards. How many cards did Andy have at the start? Write an al
    11·1 answer
  • Please help, algebra two problem
    9·1 answer
  • Using the diagram shown below, which statement is true?
    14·2 answers
  • PLEASE HELP ME WITH THIS :<
    5·2 answers
  • An angle measures 90º more than the measure of its supplementary angle. What is the measure of each angle?
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!