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
To create a table that shows how many joules of heat are required to raise the temperature of the gold bar to different temperatures, follow these steps:
1. Start with the initial temperature of the bar, which is 25°C.
2. Determine the temperature difference between the current temperature and the desired temperature.
- For example, to find the temperature difference between the current temperature of 25°C and the target temperature of 26°C, subtract 25 from 26: 26 - 25 = 1°C.
3. Multiply the temperature difference by the heat required to raise the temperature by 1°C.
- For example, using the given information, multiply 1°C by 7 joules/°C: 1°C * 7 joules/°C = 7 joules.
4. Add the heat required to reach the desired temperature to the total amount of heat required to reach the previous temperature to find the total heat required.
- For example, to find the total heat required to reach 26°C, add 7 joules (from step 3) to the initial heat of 0 joules: 0 joules + 7 joules = 7 joules.
- Similarly, to find the total heat required to reach 27°C, add 7 joules to the previous total of 7 joules: 7 joules + 7 joules = 14 joules.
5. Repeat steps 2-4 for each desired temperature to fill the table.
Using this information, you can 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 bar to a given temperature t degrees Celsius, you can use the formula:
h(t) = 7 * (t - 25)
In this equation, t represents the desired temperature in degrees Celsius. The difference (t - 25) calculates the temperature difference, and multiplying it by 7 gives the heat required in joules.