Explanation Theorem used: Separation of Variables: The solution of the differential equation, f ( y ) y ′ = g ( x ) is given implicitly by the equation, ∫ f ( y ) d y = ∫ g ( x ) d x . Formula used: Unlimited growth model: If the rate of change with respect to time t of a quantity y is proportional to the amount present, then y satisfies the differential equation, d y d t = k y , k > 0 , t > 0 Calculation: From the given data, it is observed that interest provided increases with the increase in the investment. That is, the model used is unlimited growth which has the formula, d y d t = k y , k > 0 , t > 0 . Here, the rate is 4.9%. Thus, k = 0.049 . Therefore, the unlimited growth model is, d y d t = 0.049 y . Rewrite the differential equation to the form of f ( y ) y ′ = g ( x ) as follows. d y y = 0.049 d t 1 y d y = 0.049 d t Compare the equation 1 y d y = 0.049 d t with f ( y ) y ′ = g ( x ) and observe that, f ( y ) = 1 y g ( t ) = 0.049 By the above theorem, the solution is given by, ∫ f ( y ) d y = ∫ g ( t ) d t ∫ 1 y d y = ∫ 0

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Chapter 9.2, Problem 60E

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To find: The total amount if $10,000 is invested for 4 years at the rate of 4.9% compounded continuously.

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Chapter 9.2, Problem 59E

Chapter 9.2, Problem 61E

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Chapter 9 Solutions

EBK CALCULUS FOR BUSINESS, ECONOMICS, L

Ch. 9.1 - Show that y=Cx+1 is the general solution of the...Ch. 9.1 - Prob. 2MP Ch. 9.1 - Prob. 3MP Ch. 9.1 - Prob. 4MP Ch. 9.1 - Prob. 5MP Ch. 9.1 - Prob. 1ED Ch. 9.1 - Prob. 2ED Ch. 9.1 - Prob. 1E Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E

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The total amount if $10,000 is invested for 4 years at the rate of 4.9% compounded continuously.

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To find: The total amount if $10,000 is invested for 4 years at the rate of 4.9% compounded continuously.

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