It is projected that, t years after the start of the 2020, the population of city will be P(t)=300+2t+0.3t^2 thousand people. Use increments to estimate how much the population will change during the first quarter of 2022.

Q: of tax returns that will be electronically filed for 2010 using exponential smoothing with α=0.1

A: Solution

Q: Find the effective rate of interest. For 6% compounded continuously

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Q: A student is 25 years old and the world has a population of 6.2 billion. Assuming that the…

A: Given,  Student's current age = 25 Student's future age = 68 Time (t) = 68 - 25  = 43 Annual growth…

Q: What is the total amount of 24000 TL with 4,8 % continuously compound interest after 5 years?

A: Consider the formula for continuous compounding, A=P·er·tHere,P=principalr=rate of interestt=time…

Q: Find the present value of $4000 payable at the end of 4 years, if money may be invested at 6% with…

A:

Q: Find the compound amount if $12,104 is invested at 6.2% compounded continuously for period 3 years

A: The formula used: A=Pert

Q: The half-life of carbon-14 is 5700 years. If an item is discovered with only 17% of the original…

A: Given Half life of carbon-14 =5700 years  i.e. and an item is found with only 17% of the original…

Q: Suppose that money is deposited daily into a savings account at an annual rate of $1300. If the…

A: P = $1300 r = 4% N = 4

Q: Find the exponential fulnction fGx) - Cb whose YA gaph is given..

A:

Q: Suppose the population of a city has been growing at a rate of 2.5% per year for each of the last 8…

A:

Q: A student is 19 years old and the world has a population of 6.6 billion. Assuming that the…

A: Given Present population (P) = 6.6 Rate (R) = 0.6% Time  (n) = 72-19= 53

Q: If $5000 is invested at 7% annual simple interest, how long does it take to be worth $8150? yr

A: As from the formula of simple interest, i=p×n×r100               ...(1) Where, p = principal n=time…

Q: How long does it take for $350 to grow to $840 at 6% annual percentage rate compounded continuously…

A: Continuously compounded interest formulaA= PertP = the initial principlee = natural baser = annual…

Q: The mass reaches 75 grams after t= years.

A:

Q: Find the present value of $2000 to be received in 10 years, if money may be invested at 8% with…

A:

Q: Suppose 175 trout are seeded into a lake. Absent constraint, their population will grow by 45% a…

A: At initially 175 trouts are present,Population will grow by 45% a year,Maximum trouts which can be…

Q: Find the compound amount if $12,104 is invested at 6.2% compounded continuously for each period.2…

A: Given: P=12,104  dollarsr=0.062t=2  years

Q: Because of a virus introduced into a bacterial culture, the population of the bacteria decreased…

A: Exponential decay is N = 50000e-λt Therefore, 30000 at t= 54 min Therefore 30000 = 50000e-λ54…

Q: Suppose that you have $2500 to invest at 4% compounded continuously.  The accumulated amount after…

A: Given investment amount $2500 and rate of interest r=4%=4100=0.04. Compounded continuously. The main…

Q: As an active environmentalist who is interested in the impact of climate change on sea level, you…

A: Given: Mount Kinabalu is 4095m above sea level at the beginning of year 2015 . However, due to…

Q: The half-life of Cesium-137 is 30.7 years. How long will 200 grams of Cesium-137 take to decay to…

A: Given data The half-life of the cesium-137 is t1/2 = 30.7 years. The initial amount of the…

Q: How long will it take for a principal of 1000 OMR to produce a future value of 2500 OMR at 10% rate…

A: If the interest is compounded continuously, then the formula used is A=Pert, where, A is the final…

Q: derive a formula for the of time that takes money to increase by one and half in a bank account that…

A: We have R= 3% compounded  yearly Let say it will take t years

Q: Suppose that money is deposited daily into a savings account at an annual rate of $1200. If the…

A: Compound interest problem.....

Q: The population of Northern Cascadia is growing at a rate of 20% every 3 years. Assuming that it…

A: Topic: percentage

Q: How long will it take for $4000 to double in value if it is deposited in an account bearing 7%…

A: Continuous compound interest formula: A=Pert P-principle A-Amount r-rate t-number of years.

Q: Suppose 275 trout are seeded into a lake. Absent constraint, their population will grow by 50% a…

A:

Q: As an active environmentalist who is interested in the impact of climate change on sea level, you…

A: Let Pn represents the elevation of n years for Mount Kinabalu.   At the beginning of the year…

Q: A man with ​$30,000 to invest decides to diversify his investments by placing ​$15,000 in an account…

A: Total Amount = $30,000Amount  compounded continuously =  Pertand   Amount compounded  Anually…

Q: If $4,000 is invested at 8% compounded continuously, graph the amount in the account as a function…

A: P=$4,000 , r=8%=0.08 Now by using compound interest formula for continuously compounding, we have…

Q: what is the PV of the investment. Round to the nearest cent. worth $14,000 after 4.5 years at 5.25%…

A: Given data:   *The future value of the investment is FV=$14,000. *The time taken to have the future…

Q: A principal of 7000 Rial is invested at rate 9% interest for 8 years. Determine the future value if…

A: Given, Principal Amount (P) = 7000 Rate of interest (r) = 9% Time period (t) = 8 years

Q: Suppose 200 trout are seeded into a lake. Absent constraint, their population will grow by 70% a…

A: Given problem:- Suppose 200 trout are seeded into a lake. Absent constraint, their population will…

Q: Aman with $30,000 to invest decides to diversity his investments by placing $15,000 in an account…

A:

Q: The​ half-life of​ carbon-14 is 5600 years. If a piece of charcoal made from the wood of a tree…

A:

Q: How long does it take to have a balance of $900 if $500 is invested at 0.75% annual interest…

A:

Q: A worker's salary starts at £25000 per annum and increases by £2500 every year. How long does she…

A: The initial salary of the worker is £25,000 per annum. Her salary increases by £2500 every year.…

Q: If 26 grams of radioactive waste reduces to 19.35 grams of radioactive waste after 1120 years, then…

A:

Q: A principal of RM2000 is invested at 10% interest compounded continuously. After how many days will…

A:

Q: Suppose that money is deposited daily into a savings account at an annual rate of $800. If the…

A:

Q: Find the present value of $1000 payable at the end of 3 years, if money may be invested at 8% with…

A: This is a question based on compound interest. we have to calculate on the basis of continuous…

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: 2. The population of a suburb doubled in size in an 18-month peri growth continues and the current…

A: In this question we will use basic of calculus i.e application of differential equation. We will…

Q: The half-life of carbon-14 is 5730 years. How long does it take for 2.1 grams of carbon-14 to be…

A: A(t)=A0(1/2)t/h h is the half life A0 is the initial value

Q: A principal of 7000 Rial is invested at rate 9% interest for 8 years. Determine the future value if…

A: Principal= 7000 Rial Rate of interest=9% Number of years =8

Q: The initial population of Rachtropolis is 3100 and it grows with a doubling time of 10 years.…

A:

Q: Suppose that money is deposited daily into a savings account at an annual rate of $1100. if the…

A: Given  P: the principal, =$1100 t: the time= 4 years r: the rate, (in decimal form)=0.05

Q: A bank note will be worth $76,000 when it matures in 4 years. If the note pays 3.63% per year…

A: Given:A bank note will be worth $76,000 when it matures in 4 years. If the note pays 3.63% per year…

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.