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(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

Respuesta :

carlosego
For this case we have a function of the form:
 [tex]y = A * (b) ^ x [/tex]
 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:
 [tex]200 = A * (b) ^ 0 150 = A * (b) ^ 1[/tex]
 We have a system of two equations with two unknowns.
 Dividing both equations we have:
 [tex] \frac{A * (b) ^ 1}{A * (b) ^ 0} = \frac{150}{200} [/tex]
 [tex]b = 0.75 [/tex]
 From equation 1 we have that the value of A is:
 [tex]A = 200 [/tex]
 Substituting values in the generic equation we have:
 [tex]y = 200 * (0.75) ^ x [/tex]
 Answer:
 A function that can be used to represent the relationship shown in the table is:
 [tex]y = 200 * (0.75) ^ x[/tex]
sapiji


y = 200 * (0.75) ^ x

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