Forest fires grow depending on fuel, heat, and oxygen. Wind can push the fire one way or another.
Let’s assume that our fire from the last slide is growing out from the center into a larger circle, increasing the radius of the circle by 7 miles per hour.
Create a function that tells us the length of the radius in terms of hours allowing for your initial, current radius given on the last slide, and the speed of 7 miles per hour increase.
r.
If the fire continues to spread at a pace of 7 miles per hour, how long will it take the fire to reach the burn perimeter trench created by the firefighters? Show all work to support your answer.If the fire continues to spread at a pace of 7 miles per hour, how long will it take the fire to reach the burn perimeter trench created by the firefighters? Show all work to support your answer.
To create a function that tells us the length of the radius in terms of hours, we can use the formula:
Length of radius (in miles) = initial radius + (7 miles/hour) * time
Let's assume the initial radius given on the last slide is r miles.
So, the length of the radius in terms of hours is:
Length of radius (in miles) = r + (7 miles/hour) * time
To find the time it will take for the fire to reach the burn perimeter trench created by the firefighters, we need to find the value of time when the Length of radius equals the distance of the trench from the center of the fire.
Let's assume the distance of the trench from the center of the fire is d miles.
So, we have the equation:
r + (7 miles/hour) * time = d
To solve for time, we can rearrange the equation:
(7 miles/hour) * time = d - r
Dividing both sides of the equation by 7 miles/hour, we get:
time = (d - r) / (7 miles/hour)
Therefore, the time it will take for the fire to reach the burn perimeter trench created by the firefighters is given by:
time = (d - r) / (7 miles/hour)
You need to substitute the values of r (initial radius) and d (distance of the trench from the center) into the equation to find the time in hours.