The equation I used for these are:(adsbygoogle = window.adsbygoogle || []).push({});

If N=N^{o}e^{kt}then DN/Dt=N_{0}ke^{kt}

so the two problems I have trouble with is

A radioactive substance has a decay constant (k) of -.0539 per year. If 371 grams of the material is initially present, what is the instaneous rate of change of the substance at times t=4 weeks and 18 months?

so what I did is 371(-.0539)e^{(-.0539)(4/48)=-19.907 gram/week}

and 371(-.0539)e^{(-.0539)(1.5)}=-28.421 gram/month

Is this right?

2. A radioactive substance has a half life of 23.7 days. If 4983 grams of the material is initially present, what is the instantaeous rate of change of the substance at times t=1 day

I find the k constant by -2491.5/23.7 which is -105.127 gram/day which mean -.288 gram/year? (by dividing 365). Is this right?

then for 1 day 4983(-.288)e^(-.288)(1/365)=-2.948 gram/day?

Is this right?

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# Homework Help: Instantaneous rates of change. Exponential growth and Decay

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