Problem

Model the two described quantities, state their rates, express them on a common time scale, and explain what their different output units allow to be compared.

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bacteria = B(d)=B₀·3ᵈ bacteria; savings = S(w)=S₀·50ʷ dollars, factor 50/week; common-time example = d=7w; comparison limit = both are exponential

bacteria = B(w)=B₀·3ʷ bacteria; savings = S(w)=S₀+50w dollars; common-time example = compare B(w) directly to S(w); comparison limit = the shared letter w makes quantities comparable

bacteria = B(d)=B₀·3ᵈ bacteria, factor 3 or 200% growth/day; savings = S(w)=S₀+50w dollars, rate $50/week; common-time example = after w weeks use d=7w, so B(7w)=B₀·3⁷ʷ; comparison limit = different output units mean only growth structure, not numerical dominance, is comparable

bacteria = B(d)=B₀·3ᵈ bacteria, factor 3 or 300% growth/day; savings = S(w)=S₀+50w dollars; common-time example = d=7w; comparison limit = outputs are comparable

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Model the two described quantities, state their rates, express them on a common time scale, and explain what their different output units allow to be compared.

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