## (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

0

## Answers ( No )

1. y = 200 * (0.75) ^ x

2. For this case we have a function of the form:

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:

We have a system of two equations with two unknowns.
Dividing both equations we have:

From equation 1 we have that the value of A is:

Substituting values in the generic equation we have:

Answer:

A function that can be used to represent the relationship shown in the table is: