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A sample of 400 g of lead 210 decays to polonium 210 according to the function defined by$$A(t)=400 e^{-0.032 t}$$where $t$ is time in years. Approximate answers to the nearest hundredth.(a) How much lead will be left in the sample after 25 yr?(b) How long will it take the initial sample to decay to half of its original amount?
(a) $179.73 \mathrm{g}$(b) $21.66 \mathrm{yr}$
Algebra
Chapter 12
Inverse, Exponential, and Logarithmic Functions
Section 6
Exponential and Logarithmic Equations; Further Applications
Functions
Exponential and Logarithmic Functions
Oregon State University
McMaster University
Baylor University
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So I went. Do you know how much would be left after 25 years? So that would give us a T value of 25. So it's got into our creation. You are evaluated at 25. So we're just going to replace R T with 25. That gives us a 179.73 And now for a party, we want to know how much or how long it would take, for example, to decay to half of its original. Well, the half of 400 would be 200. Okay, so let's divide both sides by 400. So we got 1/2 and now we can take the natural log on both sides. Okay, Now let's divide both sides. By this term. Here we have the natural log of 1/2 over negative 0.32 Yes. It gives us approximately a 21 points. 67
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