The amount A you get from investing k dollars after time t is given by
A(t) = k a(t)
where a(t) is the accumulation function which is given in the question to be a quadratic equation.
Hence , let the accumulation function be a(t) = αt2 + βt + γ
Note that in interest theory a(0) = 1. Thus γ = 1 (You get it when you put t=0 in the formula: a(0) = 0*α + 0*β + γ
If you invest k = $800 and accumulate $805 at t = 1 then we have the equation
805 = 800 a(4)
Similarly, if you invest k = $4000 and accumulate $4080 at t = 2 then we have the equation
4080 = 4000 a(2)
We have two equations:
4080 = 4000(4α + 2β + 1); ---eq (1) and
805 = 800(α + β + 1)----eq(2)
Solving for α and β, we get:
α = 30/8000 = 0.00375
β = 20/8000 = 0.0025
b. Putting these values in eq(1) and eq(2) we see that both the equations are satisfied, hence it is a legitimate accumulation function.
13. (10pts) Suppose that an account is governed by a quadratic accumulation function. If $800 invested...
Suppose that Po is invested in a savings account in which interest is compounded continuously at 59% per year. That is, the balance P grows at the rate given by the following equation dP 0.059P(t) dt (a)Find the function P(t) that satisfies the equation. Write it in terms of Po and 0.059. (b)Suppose that $1500 is invested. What is the balance after 2 years? (c)When will an investment of $1500 double itself? (a) Choose the correct answer below. Po P(t)...
Suppose that is invested in a savings account in which interest, k, is compounded continuously at 3% per year. The balance P(t) after time t, in years, is P(t) = Pekt a) What is the exponential growth function in terms of P and 0.03? P(t)=0
Suppose that $100,000 is invested at 5% interest, compounded annuallyA = P(1+r)' a) Find a function for the amount in the account after t years b) Find the amount of money in the account after 8 years
Question 4) Suppose that the (univariate) variable y is known to be a quadratic function of the variable x; that is, y = a x2 +bx+c, where the coefficients a, b, c are obtained by conducting an experiment in which values y1, .. , Yn of the variable y are measured for corresponding values 21,.. , Un of the variable x. Find the best least-squares fit of the quadratic polynomial using the data: {(-2,-5),(-1, -1),(0,4), (1,7), (2,6), (3,5), (4, -1)}....
Question 1: Find the Laplace Transform of the following time function (10pts) (0) 0 2 4 6 8 t (sec)
Suppose tuition is $800/course plus a $10,000 fee for
international students, i.e. 800X + 10000Y.
c) (2) Find the mean and variance of the amount of tuition a
random student pays.
d) (2) Find the probability that a random student pays at least
$4000 in tuition.
e) (2) Given that a student pays at least $4000 in tuition, find
the probability that they are an international student.
f) (2) Now suppose instead of the earlier formula, the tuition
is $800...
18. Suppose $2,900 is invested in an account at an annual interest rate of 6.6% compounded continuously. How long (to the nearest tenth of a year) will it take the investment to double in size? Answer: 19. Let f(x) = x2 - 10x + 18. (a) Find the vertex. Answer: (b) State the range of the function. Answer: (c) On what interval is the function decreasing? Answer:
Suppose that $16,416 is invested at an interest rate of 5.5% per year, compounded continuously. a) Find the exponential function that describes the amount in the account after time t, in years. b) What is the balance after 1 year? 2 years? 5 years? 10 years? c) What is the doubling time? a) The exponential growth function is P(t) = (Type exponential notation with positive exponents. Do not simplify. Use integers or decimals for any
Suppose a workstation receives parts automatically from a conveyor. An accumulation line has been provided at the workstation and has a storage capacity for 5 parts (N=6). Parts arrive randomly at the switching junction for the workstation; if the accumulation line is full, parts are diverted to another workstation. Parts arrive at a Poisson rate of 1 per minute; service time at the workstation is exponentially distributed with a mean of 45 seconds. a. What is the rate at which...
Suppose a workstation receives parts automatically from a conveyor. An accumulation line has been provided at the workstation and has a storage capacity for 5 parts (N=6). Parts arrive randomly at the switching junction for the workstation; if the accumulation line is full, parts are diverted to another workstation. Parts arrive at a Poisson rate of 1 per minute; service time at the workstation is exponentially distributed with a mean of 45 seconds.a. What is the rate at which parts...