Question

n T = 456 − 3 The equation above is used to model the relationship between the number of cups, n, of hot chocolate sold per day in a coffee shop and the average daily temperature, T, in degrees Fahrenheit. According to the model, what is the meaning of the 3 in the equation?

Answer 1

Answer:

3 represents: For every decrease of 1°F, three more cups of hot chocolate will be sold.

Step-by-step explanation:

Consider the provided equation.

$N= 456-3 T$

The relationship between the number of cups, n, of hot chocolate sold per day in a coffee shop and the average daily temperature, T, in degrees Fahrenheit.

The provided equation can be written as:

$N= -3T+456$

If we observe we can find that the above model is same as the slope intercept form $y=mx+c$. Where m is the slope.

Therefore, -3 represents the slope of the function.

The "minus" sign represents the slope of line is downward.

If we Substitute T=0 in provided equation we get N=456

That means when temperature is 0 degrees Fahrenheit the number of cups (N), of hot chocolate sold per day in a coffee shop is 456.

If we Substitute T=1 in provided equation we get N=453

If we Substitute T=-1 in provided equation we get N=459

Therefore, If we increase temperature the number of cups decreases.

Hence, the meaning of 3 in equation is: For every decrease of 1°F, three more cups of hot chocolate will be sold.