To determine To Find: The time taken to accumulate $500000 at rate 10% interest compounded continuously. Explanation Concept used: The given problem involves solving the differential equation by separating the variables, that is done as follows, d y d x = f ( x ) g ( y ) Separating the variables by bringing them in left hand side and right hand side of the equation, d y g ( y ) = f ( x ) d x Therefore the solution of this kind of the differential equation will be evaluate as, ∫ d y g ( y ) = ∫ f ( x ) d x The integral of e n x ∫ e n x d x = e n x n + c Integration by parts of two functions u and v , ∫ u v d x = u ∫ v d x − [ ∫ d u d x ∫ v d x ] Where c is called the constant of integration. When the differential equation in form of d y d x + P y = Q then, I . F = e ∫ p d x The solution of the standard form of differential equation, y ( I . F ) = ∫ Q ( I . F ) d x The amount of money is compounded continuously then it grows according to the differential equation, d A d t = r A Here, the amount of money invested is A compound interest is r and time in years is t . If some amount is deposited ( D ) continuously per year than the differential equation for growth of the account becomes, d A d t = r A + D Here, the amount of money invested is A compound interest is r , time in years is t and amount deposit per year is D . Differential equation for the given condition, d A d t = r A + D (1) Here, the amount of money invested is A compound interest is r , time in years is t and amount deposit per year is D . As given in problem no initial amount deposit i.e. ( A = 0 at t = 0 ) and deposit money in first year is $50000. Substitute ( D = $ 50000 ) and rate ( r = 0.1 ) in equation (1), then the equation becomes d A d t = 0.1 A + 50000 Separating the variables of the above differential equations, d A 0

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Chapter 10.4, Problem 3E

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To Find: The time taken to accumulate $500000 at rate 10% interest compounded continuously.

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Chapter 10.4, Problem 2E

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CALCULUS WITH APPLICATIONS

Ch. 10.1 - Find all solutions of the differential equation . Ch. 10.1 - Prob. 2YT Ch. 10.1 - Prob. 3YT Ch. 10.1 - Prob. 4YT Ch. 10.1 - Prob. 1WE Ch. 10.1 - Prob. 2WE Ch. 10.1 - Prob. 3WE Ch. 10.1 - Prob. 4WE Ch. 10.1 - Prob. 5WE Ch. 10.1 - Find the general solution for each differential...

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