Question Solved1 Answer Do n to 17. The decay of a certain substance is modelled by the function N(t) = 100(3+ e ), where the number of particles is represented by N in a time of t hours. a. What is the initial number of particles? b. Determine the rate of change in the number of particles at time t. c. How fast is the number of particles changing when t = 3 hours? %3D

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Transcribed Image Text: Do n to 17. The decay of a certain substance is modelled by the function N(t) = 100(3+ e ), where the number of particles is represented by N in a time of t hours. a. What is the initial number of particles? b. Determine the rate of change in the number of particles at time t. c. How fast is the number of particles changing when t = 3 hours? %3D
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Transcribed Image Text: Do n to 17. The decay of a certain substance is modelled by the function N(t) = 100(3+ e ), where the number of particles is represented by N in a time of t hours. a. What is the initial number of particles? b. Determine the rate of change in the number of particles at time t. c. How fast is the number of particles changing when t = 3 hours? %3D
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Step 1N(t)=100(3+e^(-t//3))(a) {:[" At the inctial time "t=0.],[" The number of particles "=N(0)=100(3+e^(-0//3))],[=100(3+1)],[=100 xx4],[=400.]:}To deztermine the rate of change of particle at fimet find the derivative of N(t) with {:[" respect tot. "],[(dN)/(dt)=(d(100(3+e^(-t//3)))/(dt)],[=(100 d(3+l^(-t//3)))/( ... See the full answer