Answer :
Consider the given differential equation
y' = 0.05y - 10,000
y' = 0.05(y - 200,000)
which is of the form y' = k(y - M)
where k = 0.05 and M = 200,000
Let f(t) be the balance in a savings account at the end of t years and suppose y f(t) satisfies t...
(1 point) John opens a bank account with an initial balance of 500 dollars. Let b(t be the balance in the account at time t. Thus b(0) 500. The bank is paying interest at a continuous rate of 4% per year. John makes deposits into the account at a continuous rate of s(t) dollars per year. Suppose that s(0) = 500 and that s(t) is increasing at a continuous rate of 2% per year (John can as his income goes...
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)...
(1 point) David opens a bank account with an initial balance of 1500 dollars. Let b(t) be the balance in the account at time t. Thus b(0) = 1500, The bank is paying interest at a continuous rate of 6% per year, David makes deposits into the account at a continuous rate of s(t) dollars per year. Suppose that s (0) 1 100 and that s (t) is increasing at a continuous rate of 5% per year (David can save...
Consider the function Let where f(t) is differentiable for all t ∈ R. Show that z satisfies the partial differential equation (x2 − y2 ) ∂z/∂x + xy ∂z/∂y = xyz for all (x, y) ∈ R2 \ { (t, 0)|t ∈ R }.
(1 point) John opens a bank account with an initial balance of 500 dollars. Let bt be the balance in the account at time t. Thus b(0)= 500. The bank is paying interest at a continuous rate of 4% per year. John makes deposits into the account at a continuous rate of s(t) dollars per year. Suppose that s(0) 500 and that s(t) is increasing at a continuous rate of 2% per year (John can save more as his income...
(h) Difference Equation Model for discrete-time systems Suppose that ylk balance of a savings account at the beginning of day k, and ulk] the amount deposited during day k. If interest is computed and added daily at a rate of +1001%), what is the balance at the beginning of day k +1? This describes the savings account as a discrete-time system on the time axis k. If the interest rate does not change with time, is the system time-invariant or...
1 point) Let a and b be constants, and let Let f(t,) . Then f is a smooth function of variables t and z, and frz Let z-W be a Wiener process. The goal is apply Ito's lemma in the form, to find a stochastic differential equation that is satisfied by Y = f(t, z) After applying Ito's lemma, dt t dz Type z Wt as z. Since Y e is a common factor on the right side, after dividing...
5. SCALCET8 4.3.068. Let (t) be the temperature at time t where you live and suppose that at time t = 5 you feel uncomfortably hot. What happens to the temperature in each case? (a) f(5) = 2,1 "(5) = -2 The temperature is increasing, and the rate of increase is increasing. Search • The temperature is increasing, but the rate of increase is decreasing. The temperature is decreasing, but the rate of change is increasing (becoming less negative). Caro...
The balance A (in dollars) in a savings account is given by A-7000ec, where t is measured in years. Find the rate at which the balance is changing when t = 1 year, t = 10 years, and 50 years. (Round your answers to two decimal places.) (a) t-1 year per year (b) t10 years per year (c)50 years per year The balance A (in dollars) in a savings account is given by A-7000ec, where t is measured in years....
Problem 1. (1 point) A function y(t) satisfies the differential equation ay = – 44 – 6y2 + 7y?. (a) What are the constant solutions of this equation? Separate your answers by commas. (b) For what values of y is y increasing? <y< Note: You can earn partial credit on this problem.