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

Answer 1

y = 200 * (0.75) ^ x

Answer 2

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:

`(A * (b) ^ 1)/(A * (b) ^ 0) = (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`