A substance has a decay rate of 4.5% per month (that is, the rate of change of an amount N of the chemical after t months is given by ð‘‘ð‘/ð‘‘ð‘¡ = -0.045ð‘). a. Suppose that 500g of the substance is present at t = 0 months. How much remains after 6 months? (4pts) b. What is the rate of change at 6 months? Show necessary steps. (6pts) c. What is the half-life of the substance? Show necessary steps. (6pts)
Added by Julian B.
Step 1
045N$$ To solve this, we can use separation of variables. Divide both sides by N and multiply both sides by dt: $$\frac{1}{N} dN = -0.045 dt$$ Now, integrate both sides: $$\int \frac{1}{N} dN = \int -0.045 dt$$ $$\ln(N) = -0.045t + C$$ Show more…
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