While Sam was at work, his house lost electrical power. By the time the electrical power came back on, the temperature inside the house was
88°F. The air conditioner immediately started to cool the house.

Let f(x) represent the temperature, in degrees Fahrenheit, of Sam’s house x minutes after the air conditioner started to cool the house.

A. What is the meaning of the statement f(30) =76?

B. Use function notation to represent the temperature of the house when the air conditioner started to cool the house.

After 30 minutes that the air conditioner started to cool Sam's house, the temperature was 76°F.

A linear equation is given by:

y = mx + b;

where m is the rate of change, y, x are variables and b is the y intercept

Let f(x) represent the temperature, in degrees Fahrenheit, of Sam’s house x minutes. the temperature inside the house was  88°F, hence b = 88

f(x) = mx + 88

Since f(30) = 76:

This means that after 30 minutes that the air conditioner started to cool Sam's house, the temperature was 76°F.

hence:

76 = m(30) + 88

m = -0.4

f(x) = -0.4x + 88

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A) 30 minutes after the air conditioner started to cool the house, the temperature inside the house has dropped to 76°F

B)

Step-by-step explanation:

A)

In this problem, f(x) represents temperature, in degrees Fahrenheit, of Sam’s house x minutes after the air conditioner started to cool the house.

So we have:

x = minutes after the air conditioner started to cool the house

f(x) = temperature

Here we want to find what is the meaning of

Which implies that:

, which means that 30 minutes have passed after the conditioner has started to cool the house

, which means that the temperature of the room at that time is 76°F

So, the interpretation of f(30) =76 is that:

"30 minutes after the air conditioner started to cool the house, the temperature inside the house has dropped to 76°F"

B)

Here we want to write explicitely a function that tells us how the temperature inside the house varies as a function of x, the number of minutes passed after the air conditioner has turned on.

We know the following information:

- At time x = 0, the temperature inside the house is 88°F

- At time x = 30 min, the temperature inside the hosue is 76°F

We can assume that the temperature inside the house changes linearly with time; so, we can describe the temperature function with the equation of a line:

where

is the value of the temperature at x = 0, so q = 88

m is the rate of change of the temperature

The rate of change can be found by calculating the rate of change of the temperature with respect to the change in time; so we find:

which means that the temperature decreases by 0.4°F every minute. So, the function can be written as

20335+282=20617

step-by-step explanation: