Problem

Use the displayed graphs to interpret \(S(t)=40(0.7)^t+10\). Identify the baseline and excess concentration, evaluate \(S(0)\), describe the decay of the excess, and determine the long-run concentration and asymptote.

Unannotated graph of S(t)=40(0.7)^t+10 parts per million; the curve begins at 50 and approaches 10, but baseline and component labels are withheld.

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Baseline 10 ppm per interval; component 40(0.7)t ppm; S(0) = 50 ppm; 10 ppm are added every interval; the long-run concentration increases without bound.

Baseline 50 ppm; component 40(0.7)t ppm; S(0) = 50 ppm; the component decays toward 0; the long-run concentration and horizontal asymptote are 50 ppm.

Baseline 10 ppm; component 40(0.7)t ppm; S(0) = 50 ppm; the component grows without bound; the long-run concentration is 10 ppm.

Baseline 10 ppm; component 40(0.7)t ppm; S(0) = 50 ppm; the component decays toward 0; the long-run concentration and horizontal asymptote are 10 ppm.

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Use the displayed graphs to interpret \(S(t)=40(0.7)^t+10\). Identify the baseline and excess concentration, evaluate \(S(0)\), describe the decay of the excess, and determine the long-run concentration and asymptote.

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