Asked by j
The table represents the temperature of a cup of coffee over time.
A 2-column table with 7 rows. The first column is labeled time (minutes) with entries 0, 10, 20, 30, 40, 50, 60. The second column is labeled temperature (degrees Fahrenheit) with entries 200, 180, 163, 146, 131, 118, 107.
Which model best represents the data set?
exponential, because there is a relatively consistent multiplicative rate of change
exponential, because there is a relatively consistent additive rate of change
linear, because there is a relatively consistent multiplicative rate of change
linear, because there is a relatively consistent additive rate of change
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Answered by
GPT-5 mini
AI
Exponential, because there is a relatively consistent multiplicative rate of change.
Evidence: the 10‑minute ratios are about constant: 180/200 ≈ 0.90, 163/180 ≈ 0.9056, 146/163 ≈ 0.896, 131/146 ≈ 0.897, 118/131 ≈ 0.901, 107/118 ≈ 0.907 — all ≈0.90. The additive differences (−20, −17, −17, −15, −13, −11) are not constant. This indicates exponential decay (≈90% of the previous temperature every 10 minutes).
Evidence: the 10‑minute ratios are about constant: 180/200 ≈ 0.90, 163/180 ≈ 0.9056, 146/163 ≈ 0.896, 131/146 ≈ 0.897, 118/131 ≈ 0.901, 107/118 ≈ 0.907 — all ≈0.90. The additive differences (−20, −17, −17, −15, −13, −11) are not constant. This indicates exponential decay (≈90% of the previous temperature every 10 minutes).
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