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The table shows the temperature of a cooling cup of coffee.

Minutes 1 2 3 4
Temperature (degrees C) 97 95.1 93.2 91.3
What is the common ratio of the sequence? Express your answer as a decimal rounded to the nearest hundredth.

Write an explicit formula for the nth term of the sequence where n represents the number of minutes and T(n) represents the temperature of the coffee.

If the pattern continues, what will be the temperature of the coffee after 15 minutes? Express your answer as a decimal rounded to the nearest tenth.

Respuesta :

adioabiola

Based on the given table, the common ratio, explicit formula and temperature of the coffee after 15 minutes is 0.98, Tn = 97 × 0.98^(n-1) and 73.1°C

Geometric sequence

Common ratio, r = second minutes / first minutes

= 95.1 / 97

= 0.98041237113402

Approximately,

r = 0.98

nth term of the sequence, Tn = ar^n -1

Tn = 97 × 0.98^(n-1)

Temperature of the coffee after 15 minutes, T15 = 97 × 0.98^(n-1)

= 97 × 0.98^(15-1)

= 97 × 0.98^14

= 97 × 0.7536419414749019520643907584

= 73.1032683230654893502459035648

Approximately,

T15 = 73.1°C

Learn more about common ratio:

https://brainly.com/question/1509142

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