The temperature at sunrise is 65 degreesF. Each hour during the day, the temperature rises 5 degreesF. Write an equation that models the temperature y, in degrees Fahrenheit, after 4 hours during the day.
now: temp = 65
after 1 hour temp = 65 + 5(1)
after 2 hours temp = 65 + 5(2)
after 3 hours temp = 65 + 5(3)
...
after x hours temp = 65 + 5x
The tem perature at sunrise is 65°F. Each hour during the day, the
tem perature rises 5°F. Write an equation that models the tem perature y, in degrees
Fahrenheit, after x hours during the day. What is the graph of the equation?
Sure! Let me put on my math hat and come up with a hilarious equation for you:
y = 65 + (5 * 4)
In simpler terms, the temperature after 4 hours can be modeled by adding 65 degrees Fahrenheit to the product of 5 degrees Fahrenheit and 4 hours.
But hey, don't let the equation fool you! It's just math being serious while we're having all the fun.
To write an equation that models the temperature after 4 hours during the day, we need to start with the initial temperature at sunrise and account for the temperature increase every hour.
Let's denote the initial temperature at sunrise as T₀ and the temperature increase per hour as ΔT. In this case, T₀ = 65 degrees Fahrenheit and ΔT = 5 degrees Fahrenheit.
We can use the formula for linear relationships to write the equation:
y = T₀ + ΔT * t
Where:
- y represents the temperature after t hours during the day.
In this case, we need to find the temperature after 4 hours, so we substitute t = 4 into the equation:
y = 65 + 5 * 4
y = 65 + 20
y = 85
Therefore, the equation that models the temperature after 4 hours during the day is:
y = 85 degrees Fahrenheit.
To write an equation that models the temperature after 4 hours during the day, we can start with the initial temperature at sunrise and then add the increase in temperature for every hour that passes.
Given that the initial temperature at sunrise is 65 degrees Fahrenheit and the temperature rises by 5 degrees Fahrenheit every hour, we can express the equation as:
y = 65 + 5(4)
Let me explain how I arrived at this equation:
1. We start with the initial temperature at sunrise, which is given as 65 degrees Fahrenheit.
2. We know that the temperature rises by 5 degrees Fahrenheit every hour. Since 4 hours have passed, we need to add this increase to the initial temperature.
3. To calculate the increase in temperature after 4 hours, we multiply the hourly increase (5 degrees) by the number of hours (4), which gives us 20 degrees Fahrenheit.
4. Finally, we add the increase in temperature (20 degrees) to the initial temperature at sunrise (65 degrees) to get the final temperature after 4 hours during the day, which is represented by the variable y.
So, the equation that models the temperature after 4 hours during the day is:
y = 65 + 5(4)
Simplifying this equation, we have:
y = 65 + 20
y = 85
Therefore, the temperature after 4 hours during the day would be 85 degrees Fahrenheit.