What constant interest rate is required if an initial deposit placed into an account accrues interest compounded continuously is to double its value in six years? `(ln|x|=0. 6930)`

What will Rs. 500 amounts to in 10 years after its deposit in a bank which pays annual interest rate of 10% compounded annually?

If an initial amount A_(0) of money is invested at an interest rate r compounded n times a year, the value of the investment after t years is A=A_(0)(1+1/n)^(nt) . If the interest is compounded continuously, (that is as ntooo ), show that the amount after t years is A=A_(0)e^(rt) .

Express each of the following physical statements in the form of differential equation. (iv) A saving amount pays 8% interest per year, compounded continuously. In addition, the income from another investment is credited to the amount continuoulsy at the rate of Rs. 400 per year.

In a bank, principal increases continuously at the rate of r% per year.Find the value of r if Rs 100 double itself in 10 years (log_(e)2 = 0.6931) .

The rate constant of a first order reaction is 2.0xx10^(-6)s^(-1) . The initial concentration of the reactant is 0.10 "mol dm"^(-3) . What is the value of the initial rate ?

A person deposits Rs. X in savings bank account at the rate of 5% per annum and Rs. Y in fixed deposit at 10% per annum. At the end of one year, he gets Rs. 400 as total interest. If he deposits Rs. Y in savings bank account and Rs. X in fixed deposit, he would get Rs. 350 as total interest. Find the total amount he deposited.

Radon-222 is a radioactive gas for which the decay constant is 2.1xx10^(-6)s^(-1) . If the initial decay rate is 5.6xx10^(10)s^(-1) , calculate : (i) the initial number of radioactive atoms present and (ii) the time which will elapse before the activity is reduced to one-quarter of its initial value. Given : log_(e)2=0.693 .

A country has a food deficit of 10%. Its population ear. Its annual food production every year is 4% more than that of the last year Assuming that the average food requirement per person remains constant, prove that the country will become self-sufficient in food after n years, where n is the smallest integer bigger than or equal to (log_e 10-log_e 9)/((log_e 1.04)-0.03)