A factory produced Q(L)= 9L^(2/3) items each day, where L is the size of the labor force in worker-hours. Currently, the factory employs 8,000 worker-hours each day. Use increments to estimate the number of additional worker-hours that would be required to increase daily output by 130 items.

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: What is the total amount of 4500 TL with 3,7 % continuously compound interest after 3 years?

A: Given Present value (P)= 4500 TL Rate (r)=3.7% Number of years (t)= 3

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 effective rate of interest.For 5% compounded continuously

A: Here we have to find the effective rate of interest. For 5% compounded continuously.  r = 5%…

Q: Suppose the population of a certain bacteria in a laboratory sample is 100. If it doubles in…

A: The initial population of the bacteria is, P0=100. After every t=6, the population doubles. So, the…

Q: odine -131 has a half-life of approximately 8 days. ind the amount of iodine-131 left from a 100…

A:

Q: To get $800 after 212years at 8% compounded continuously

A: $800 after 212 years at 8% compounded continuously.

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: what annual ratte of interst compounded annually is required to double an investment in 9 years?…

A:

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: Today there are 500 ants on an colony. They breed with a constant continuous growth rate of 20% per…

A: We will find out the required solution.

Q: What rate is required to grow 750 to 7500 in 14 years?

A:

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: Find the volume of the largest cube of wood that can be cut from a log of circular cross section…

A: Given that, the radius of circular cross section is 6 inch.

Q: Find the time needed to double an investment at 8% annual interest rate compounded continuously.

A:

Q: solve for y: ln(3-y)-ln(y) = 2x + ln(5) without a calculator

A: Given equation is :Moving all the logarithm terms and using the property: ln(a) – ln(b) =…

Q: A quantity with an initial value of 850 grows continuously at a rate of 90% per decade. What is the…

A: Given: A quantity with an initial value of 850 grows continuously at a rate of 90% per decade. To…

Q: Determine how much time is required for an investment to triple in value if interest is earned at…

A: Let P be the principal amount, then the triple amount of P is 3P.

Q: A material decays at the rate of 0.099% per year. How long will the material take so that only 30%…

A:

Q: If an initial population Po of bacteria doubles in 6 hours, how long will it take to triple (grow to…

A: Given that  6 hours to take doubles the initial population

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

A: Compound interest problem.....

Q: Suppose a computer that costs $1,000 decreases in value by 17% each year. The estimated value of the…

A:

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: Differentiate  y = ln(2x + 1)

A:

Q: Differentiate  y = ln(4x2 - 2x + 9)

A: To differentiate  y=ln(4x2-2x+9) The given function is a composite function, Hence, let u=4x2-2x+9…

Q: An investment earns 5.1% yearly interest compounded continuously and is currently growing at the…

A: Solution:Given    i=5.1%     n=1     A=765   To find P=?Formula:A=P(1+i)n

Q: What are two ways to write the increment of work?

A:

Q: Determine how long it will take for an initial investment to double if it earns 7% interest per year…

A: The time take to double the initial investment is approximately 10 years  see the calculation below

Q: The population in India was 952108000 in 1996 and was growing at a rate of 1.3% per year. What will…

A:

Q: Suppose that money is deposited daily into a savings account at an annual rate of $1400. If the…

A:

Q: see attached

A:

Q: Find the time required for an investment of $9000 to grow to $25000 at an annual interest rate of 5%

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Q: What initial investment at 8% compounded continuously for 5 years will accumulate to $50, 000?

A:

Q: Find the interest rate r needed for an investment of $5000 to grow to $8000 in 8 years if interest…

A:

Q: A quantity with an initial value of 8200 grows continuously at a rate of 0.55% per decade. What is…

A: Initial Value=  8200. Growth rate= 0.55% . We can formulate the following equation for "t" years :…

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

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 quantity with an initial value of 3600 grows continuously at a rate of 2.5% per decade. What is…

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: Find the accumulated amount after 5 years if $4500 is invested at 4%/year compounded continuously.

A:

Q: What is the annual yield for an investment that earns 7% intrest compounded semianually?

A: We have given Interest rate, r = 7% = 0.07 Number of compounding periods, n = 2 (semiannually)

Q: Find the interest rate needed for an investment of $3,000 to grow to an amount of $4,000 in 4 yr if…

A:

Q: $3,500 is invested at a rate of 6% coumpounded weekly. What is the amount at the end of 15 years?

A: Principal amount P = $3500 Rate r = 6% weekly             =( 6/52)% annually  Time t = 15 years  =…

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

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.