3. A student borrows $20,000 to go to UTT to study Civil Engineering. Theannual interest rate on the loan is 5% and she agrees to make payments atthe rate of $1000 per month.Given that y(t) represents the amount the student owes at any time t inmonths. the differential equation representing the situation is:dydt0.0512y-1000 and y(0) = 20,000Solve the differential equation to determine how long it will take for thestudent to pay off the loan.4. Solve the following homogeneous first order differential equation(4y+ 3x)dydx= =3x-y

Answered: Image /qna-images/answer/1707975c-e1a1-41a9-95cb-64f646d9d05f.jpg

Answered: homogeneous first order differential…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section6.1: Exponential Functions

Problem 60SE: The formula for the amount A in an investmentaccount with a nominal interest rate r at any timet is...

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An evergreen nursery usually sells a certain shrub after 6 years if growth and shaping. The growth rate during those 6 years is approximated by "(dh)/(dt)=3.5t+9" where "t" is the time in years and "h" is the height in centimeters. The seedlings are 15 centimeters tall when planted ("t=0"). How tall are the shrubs when they are sold? A. 165 cm B. 78 cm C. 132 cm D. 270 cm
Please answer with illustration and handwritten solution. A dirty lake was contaminated by a toxic substance. The lake has a volume of 100,000 liters of water with 9k lbs of the toxic substance. To solve this problem, they intentionally pour 1,000 liters of pure clean water per hour and release the toxic water with the same rate. a. find its differential equation. b. amount of toxic after a day.
UCLAium-1919 is a radioactive element with a half-life of 140 days. Suppose that 10 mg of the element are placed in a lead container. Let y(t) represent the number of mg present t days later. Give exact answers only for all parts. No decimals, no rounding. The equation that represents the number of mg present t days later is y(t) = How many mg will be present after 10 weeks? Answer = In how many days will it take for 70% of the original sample to decay? Answer =
In 2007, (when t = 0), world solar photovoltaic (PV) market installations were 2826 megawatts and were growing exponentially at a continuous rate of 48% per year. Write a differential equation to describe the relationship in the form of dS/dt.
An investor deposits an initial amount of money (Yo) into a bank account that offers a simple (annually compounding) interest rate (r). The bank charges a fixed annual fee (b). The bank charge is debited after the interest is accumulated. Write down a difference equation that describes how the account balance (Yt) changes over time (t), then solve the equation analytically. If the interest rate is r = 0.1(10%), the bank charge is b = 100 and the investor projects that the account balance in year t = 3 is $2,464, then the %3D initial amount of money is: Select one: Select one: O yo = $2,000 O yo = $2, 100 O yo = $2, 200 O yo = $1,900
A radioactive material decays at a rate which is proportional to the amount of radioactivity remaining. If the amount of radioactivity remaining is denoted by N at the time t, form an equation which represents this statement. If the half-life (the time taken for half the radioactivity to decay) is 10 years, how long will it take for ¾ of the radioactivity to decay?
If the growth rate of the number of bacteria at any time (t) is proportional to the number present at (t) and doubles in 1 week, how many bacteria can be expected after 18 days if the initial amount is 1000?
When you turn 50 you have $600, 000 in a retirement account which receives 5% annually. You plan to withdraw $50, 000 each year. (a) Set up and solve a differential equation for the balance in P(t), the amount in the retirement account after t years. (b) Estimate the number of years your retirement fund will last.
The spread of a rumor in a group of people can be modeled by a logistic growth equation. In a business of 1000 employees, if 10% of the employees have heard the rumor at time t = 0 days and the number of people who have heard the rumor is growing at a rate of 120 employees/day at that time (hint: useful for finding r), find a differential equation to model this situation and solve it to find a formula for the number of employees who have heard the rumor at time t. Sketch the phase graph for your equation and clearly identify any equilibrium points and classify them by type.
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