6.7Exponential and Logarithmic Models

The integrated first-order law [A]ₜ = [A]₀e^(−kt) is algebra §6.8's continuous decay model A = A₀e^(rt) with r = −k under a different variable name, and once a student has solved 6.8's exponential decay problems, every half-life and time-to-decompose example in this section is the identical calculation with concentration standing in for amount.

This section and algebra §6.8 solve the identical problem from opposite sides — the half-life formula t½ = ln2/λ is 6.8's continuous decay model A = A₀e^(rt) with r = −λ, and 6.8 already uses carbon-14 and uranium-235 as its own worked examples, so a student who has done 6.8's decay problems has effectively already performed this section's decay-constant calculations.