A jeweler is heating a gold bar. It takes 7 joules of heat
to raise the temperature of the bar 1°C. The initial
temperature of the bar is 25°C. Use this information
for Items 4–11.
4. Make a table that shows how many joules of heat
would be required to raise the temperature of the
gold bar to 26°C, 27°C, 28°C, 29°C, 30°C, and
35°C.
5. Write the equation of a function h(t) that
represents the amount of heat in joules required
to heat the bar to a temperature of t degrees
Celsius.
please explain step by step
so far i think im suppoesd to add 7 to 25 and keep going
yuj
To create the table, we need to calculate the amount of heat required to raise the temperature of the gold bar from 25°C to each given temperature.
Step 1: Calculate the temperature difference for each scenario.
For 26°C: 26°C - 25°C = 1°C
For 27°C: 27°C - 25°C = 2°C
For 28°C: 28°C - 25°C = 3°C
For 29°C: 29°C - 25°C = 4°C
For 30°C: 30°C - 25°C = 5°C
For 35°C: 35°C - 25°C = 10°C
Step 2: Calculate the amount of heat required for each temperature difference.
For a temperature difference of 1°C: 1°C x 7 joules/°C = 7 joules
For a temperature difference of 2°C: 2°C x 7 joules/°C = 14 joules
For a temperature difference of 3°C: 3°C x 7 joules/°C = 21 joules
For a temperature difference of 4°C: 4°C x 7 joules/°C = 28 joules
For a temperature difference of 5°C: 5°C x 7 joules/°C = 35 joules
For a temperature difference of 10°C: 10°C x 7 joules/°C = 70 joules
Step 3: Create the table.
| Temperature (°C) | Heat Required (joules) |
|------------------|-----------------------|
| 26°C | 7 |
| 27°C | 14 |
| 28°C | 21 |
| 29°C | 28 |
| 30°C | 35 |
| 35°C | 70 |
Now let's move on to writing the equation of the function.
To represent the amount of heat required to heat the bar to a temperature "t" degrees Celsius, let's consider that the initial temperature is 25°C and it requires 7 joules of heat to raise the temperature by 1°C. We can use the equation of a linear function:
h(t) = mx + b
where h(t) is the heat in joules required to raise the temperature to "t" degrees Celsius, m is the slope of the line (amount of heat required per degree Celsius), x is the temperature difference between "t" and the initial temperature (25°C), and b is the y-intercept (amount of heat required at the initial temperature, which is 25°C).
In our case, the slope (m) is 7 joules/°C, and the y-intercept (b) is 0 joules since it does not require any additional heat at the initial temperature.
Therefore, the equation of the function is:
h(t) = 7t + 0
or simply
h(t) = 7t
To create a table showing how many joules of heat would be required to raise the temperature of the gold bar to various temperatures, you can follow these steps:
1. Note the initial temperature of the gold bar, which is given as 25°C.
2. Determine the temperature increase for each step. In this case, it is 1°C since the bar is being raised by 1 degree at a time.
3. Start with the initial temperature of 25°C and add the temperature increase for each step to get the desired temperature values.
Now, let's create the table:
| Temperature (°C) | Heat Required (joules) |
|------------------|-----------------------|
| 26 | 7 |
| 27 | 14 |
| 28 | 21 |
| 29 | 28 |
| 30 | 35 |
| 35 | 70 |
To write the equation of a function h(t) that represents the amount of heat in joules required to heat the gold bar to a temperature of t degrees Celsius, we observe that the relationship between temperature and heat is linear, with a constant rate of 7 joules per 1°C increase.
The equation can be written as:
h(t) = 7(t - 25)
Here, t represents the desired temperature in degrees Celsius and h(t) represents the amount of heat required in joules. By plugging in different values of t into the equation h(t), you can determine the specific amount of heat required for each temperature.