Lat Po is invested in a savings account where intere Express P(t) in terms of P where 0.031 is the rate en will an investment of $2500 double itself?

Q: Over 4 years, researchers studied the growth of a fish population and found its growth rate to P'(t)…

A: hintddxtan-1x=11+x2 or,∫11+x2dx=tan-1x

Q: Suppose $5,000 is invested at 7% intrest compounded continiously. How long will it take the…

A: The investment amount P = $ 5000. The interest rate r = 7% compounded continuously. The final amount…

Q: d) A population of 100 bacteria decays at a rate of 5% each day How many bacteria, y, will there be…

A:

Q: You have 500-grams of an unknown radioactive substance that has been determined to decay according…

A: D(t) = 500e-0.001904.tLet substance take x years to become half of the initial ammount.After x years…

Q: How many years will it take for an initial investment of $30,000 to grow to $75,000? Assume a rate…

A: An initial investment (P) compounded continuously with a rate of interest (r) in time (t) will grow…

Q: (b) Find the instantaneous rate of change of g with respect to x at x = 3, or state that it does not…

A: 3. given graph of function is                                                       Also,…

Q: ) The population of the world in 2015 was 9.75 billion people and was growing at a rate of 25% per…

A: Given query is to find the expression for the population after t years.

Q: The amount of carbon 14 remaining in a sample that originally contained A grams is given by C(t) =…

A: The amount of carbon 14 remaining in a sample that originally contained A grams is given bt…

Q: An initial amount of $1900 is invested in an account at an interest rate of 8% per year, compounded…

A:

Q: f. Assume that the population of a certain city increases at a rate proportional to the number of…

A: Note: Since the image contains multiple questions, as per the answering guidelines we are to solve…

Q: A certain drug is eliminated from the bloodstream with a​ half-life of 34 hours. Suppose that a…

A:

Q: If f10,500 is invested fie 3 4ears at a rate of 9%.how much willyou have if interest Es compounded…

A: P=10500t=3 years.r=9%=0.09To find A

Q: 2. Assuming no withdrawals during the investment, how many years will it take for $500, invested at…

A:

Q: Suppose that a chemical reaction proceeds according to the law of growth and decay. If half the…

A:

Q: At the time of the birth of a child, a parent wants to begin a college fund that will grow to $43000…

A: Given that the interest is compounded continuously

Q: How long will it take to triple $12000, invested at 4.5% compounded continuously? (A = Pe*t) %3D

A: We are given the initial value to be $12000 and rate r = 4.5% = 0.045. Now, we need to find that how…

Q: |81. Recall that the present value (PV) of an investment that pays out income continuously at a rate…

A: The present value (PV) of an investment that pays out income continuously at a rate R(t) for T years…

Q: At what nominal rate compounded continuously must money be invested to double in 6 years? A rate of…

A: We will solve the problem

Q: The population of the world in 2015 was 9.75 billion people and was growing at a rate of 1.25% per…

A: Given population of world in 2015  was 9.75 billionlet   for t=0 , we have year 2015

Q: A 10 year continuous annuity pays at a rate of t at time t. If v^t = .94t, calculate the accumulated…

A:

Q: A CERTAIN RADIOACTIVE MATERIAL IS KNOWN TO DECAY AT A RATE PROPORTIONAL TO THE AMOUNT PRESENT. IF…

A: Given that, after one hour, the 10% of the material is decayed. find the expression of the material…

Q: 5. Consider a scenario in which a 20ft tall lamppost lights up a street. A 5ft tall woman stands…

A:

Q: 10. How long will it take you to reach $4000 compounded continuously if you invested the $5200 at…

A: A=$5200, P=$4000, r=4.7%=0.047

Q: An environmentalist finds that a certain type of tree grows in such a way that its height h(t) after…

A: The rate at which the height of the tree changes is given by,h'(t)=3t2+t    ft/yr…

Q: If the instantaneous growth rate of COVID19 is modeled by (limHh->0)(200t+100h). At t=5 seconds…

A:

Q: certain radioactive material is known to decay at a rate proportional to the amount present. If…

A: We will solve the radioactive decay problem.

Q: If $P is invested for n years at 10% compounded continuously, the future value that results after n…

A:

Q: A forester finds that a certain type of forest tree grows in such a way that its height h(t) after t…

A:

Q: Find the present value of a continuous income stream F(t) = 40 + 5t, where t is in years and F is in…

A:

Q: Find the PV of an income stream that pays out continuously at a rate of R(t) = 3000e0.1r dollars per…

A:

Q: Find the present value Po of each amount P due t years in the future and invested at interest rate…

A: Given: The amount P= $100,000 The time is t= 6 years. The rate of interest is k=3%

Q: 2. The population of the earth was 3 billion in 1970 and was increasing at a rate of 2% per year.…

A:

Q: A certain drug is eliminated from the bloodstream with a half-life of 34 hours. Suppose that a…

A: Exponential decay formula: - The amount drops gradually, followed by a quick decrease in the rate of…

Q: The population of the world in 2015 was 9.75 billion people and was growing at a rate of 1.25% per…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: The amount of radio active material present at time t is given by A=Aoe*t, where Ao is the initial…

A: As many Questions are given , I will solve only one: Let A0 be the initial amount. Given that a…

Q: 4. A bank pays interest continuously at the rate of 6%. How long does it take for a deposit of Qo to…

A:

Q: In the future value of $1000 invested for n years at 12%, compounded continuously, is given by S=…

A:

Q: A company is considering expanding their production capabilities with a new machine that costs…

A: Cost of new machine = 53,000 Investment = 53000 Rate of interest, r= 0.7% per year = 0.007 Time = 9…

Q: g) For how long do we have to invest $1000 at a rate of 2.5% compounded continuously to obtain a…

A:

Q: How long it will take $5,000 to be double, when invested at an annual interest rate of 4% if the…

A: Given query is to find the time taken toake an invy double when interest rate is 4% and compounding…

Q: Suppose Shunreca Garner invested $8000 in stocks and the investment grew exponentially to $10000 in…

A: To use the exponential model to 1) determine the  growth rate and 2) to calculate the value after 15…

Q: Find the PV of an income stream that pays out continuously at a rate of R(t) = 3000e0.1" dollars per…

A: Given problem:- Find the PV of an income stream that pays out continuously at a rate of R(t) =…

Q: How long will it take to double your money if it is invested at a fixed interest rate of 6%…

A:

Q: A money market fund has a continous flow of money at a rate of f(x)=0.07x+700 for 10 years. Find the…

A:

Q: A radioactive element decays according to the function Q= Qn e", where Q, is the amount of the…

A: Given that a radioactive element decays according to the function Q=Q0ert, where Q0is the amount of…

Q: 2. At what rate of interest, compounded continuously will an investment double in six years? 3.…

A: (2) given that the principle amount will gets doubled in six years if the amount is compounded…

Q: Suppose an Egyptian mummy is discovered in which the amount of carbon-14 present is only about…

A:

Q: b) Let at time t years, an industry consumes fuel at the rate of (2t + 9) million barrels per year.…

A: Given an industry consumes fuel at the rate of 2t+912 million barrels per year. If the total supply…

Q: An investor has $4000 to invest in either a bond that matures in 4 years or a business that will…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.