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An investment pays 8% interest compounded continuously. If money is invested steadily at the rate of $18,000, how much time is required until the value of the investment reaches $180,000? The amount of time required is approximately years. (Type an integer or decimal rounded to the nearest hundredth as needed.) View an Example Question Help An investment pays 8% interest compounded continuously. If money is invested steadily at the rate of $15,000, how much time is required until the value of the investment reaches $150,000? KeN-t)dt = 15.000 e0.08(N -t)dt Integrate with respect to t. 15,000 e 0.08(N-t)dt = - 187.500 e0.08(N - 1)| Now, set the definite integral equal to the ending balance and isolate the exponential term. = 150,000 - 187,500 e0.08(N - t)N - 187,500 (e0- 0.08N) = 150,000 0.08N = 1.8 Take the natural logarithm of both sides and solve for N. 0.08N = 1.8 0.08N = In (1.8) N 7.35 The amount of time required is approximately 7.35 years.

An investment pays 8% interest compounded continuously. If money is invested steadily at the rate of $18,000, how much time is required until the value of the investment reaches $180,000? The amount of time required is approximately years. (Type an integer or decimal rounded to the nearest hundredth as needed.) View an Example Question Help An investment pays 8% interest compounded continuously. If money is invested steadily at the rate of $15,000, how much time is required until the value of the investment reaches $150,000? KeN-t)dt = 15.000 e0.08(N -t)dt Integrate with respect to t. 15,000 e 0.08(N-t)dt = - 187.500 e0.08(N - 1)| Now, set the definite integral equal to the ending balance and isolate the exponential term. = 150,000 - 187,500 e0.08(N - t)N - 187,500 (e0- 0.08N) = 150,000 0.08N = 1.8 Take the natural logarithm of both sides and solve for N. 0.08N = 1.8 0.08N = In (1.8) N 7.35 The amount of time required is approximately 7.35 years.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.3: The Natural Exponential Function
Problem 38E
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An investment pays 8% interest compounded continuously. If money is invested steadily at the rate of $18,000, how much time is required until the value of the investment reaches $180,000? The amount of time required is approximately years. (Type an integer or decimal rounded to the nearest hundredth as needed.) View an Example Question Help An investment pays 8% interest compounded continuously. If money is invested steadily at the rate of $15,000, how much time is required until the value of the investment reaches $150,000? KeN-)dt =15,000 e ,0.08(N-t)dt r(N Integrate with respect to t. 15,000 e e0.08(N - t) 0.08(N-1) dt = - 187,500 0.08(N – 1)| Now, set the definite integral equal to the ending balance and isolate the exponential term. = 150,000 %3D -187,500 e0.08(N-1) - 187,500 (e- e0.08N) = 150,000 %3D 0.08N = 1.8 Take the natural logarithm of both sides and solve for N. 0.08N = 1.8 0.08N = In (1.8) N 7.35 The amount of time required is approximately 7.35 years.
Transcribed Image Text:An investment pays 8% interest compounded continuously. If money is invested steadily at the rate of $18,000, how much time is required until the value of the investment reaches $180,000? The amount of time required is approximately years. (Type an integer or decimal rounded to the nearest hundredth as needed.) View an Example Question Help An investment pays 8% interest compounded continuously. If money is invested steadily at the rate of $15,000, how much time is required until the value of the investment reaches $150,000? KeN-)dt =15,000 e ,0.08(N-t)dt r(N Integrate with respect to t. 15,000 e e0.08(N - t) 0.08(N-1) dt = - 187,500 0.08(N – 1)| Now, set the definite integral equal to the ending balance and isolate the exponential term. = 150,000 %3D -187,500 e0.08(N-1) - 187,500 (e- e0.08N) = 150,000 %3D 0.08N = 1.8 Take the natural logarithm of both sides and solve for N. 0.08N = 1.8 0.08N = In (1.8) N 7.35 The amount of time required is approximately 7.35 years.
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