(100+ POINTS) A fresh cup of coffee is placed on a table to cool. The table below shows the relationship between the temperature of t

Question

(100+ POINTS)
A fresh cup of coffee is placed on a table to cool. The table below shows the relationship between the temperature of the coffee, y, as it relates to time in minutes, x.

Time (minutes), x 0 1 2 3
Temperature (F°), y 200 150 112.5 84.375

Which function can be used to represent the relationship shown in the table?
y = (0.75) x
y = 0.75(200) x
y = 200(-0.75) x
y = 200(0.75) x

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Answers ( No )

    0
    2021-09-19T05:30:27+00:00

    y = 200 * (0.75) ^ x

    0
    2021-09-19T05:30:30+00:00

    For this case we have a function of the form:
     y = A * (b) ^ x
     Where,
     A: initial temperature
     b: rate of change
     x: time in minutes
     y: temperature
     We must find the values of the constants A and b.
     To do this, substituting values we have:
     200 = A * (b) ^ 0  150 = A * (b) ^ 1
     We have a system of two equations with two unknowns.
     Dividing both equations we have:
      \frac{A * (b) ^ 1}{A * (b) ^ 0} = \frac{150}{200}
     b = 0.75
     From equation 1 we have that the value of A is:
     A = 200
     Substituting values in the generic equation we have:
     y = 200 * (0.75) ^ x
     Answer:
     
    A function that can be used to represent the relationship shown in the table is:
     
    y = 200 * (0.75) ^ x

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