Evaluate with nth Roots.
For mammals, the lung volume V ( in milliliters) can be modeled by V=170m^4/5 where m is the body mass ( in kilograms)/ Find the lung volume of each mammal.
Mongoose - Body Mass(kg) = 1.14
Camel - Body Mass (kg) = 229
To find the lung volume for each mammal, we will substitute their body masses into the given formula:
For Mongoose (m = 1.14 kg):
V = 170 * (1.14)^4/5
To evaluate this expression, we need to find the fifth root of (1.14)^4. Let's calculate it step-by-step:
Step 1: Calculate (1.14)^4
(1.14)^4 ≈ 1.857
Step 2: Find the fifth root of 1.857. This can be done by raising 1.857 to the power of 1/5:
1.857^(1/5) ≈ 1.165
Now we can substitute this value back into the original formula to calculate the lung volume for the Mongoose:
V ≈ 170 * 1.165 ≈ 198.05 milliliters
Therefore, the lung volume of the Mongoose is approximately 198.05 milliliters.
For the Camel (m = 229 kg):
V = 170 * (229)^4/5
Similarly, let's evaluate this expression step-by-step:
Step 1: Calculate (229)^4
(229)^4 ≈ 1,461,214,441
Step 2: Find the fifth root of 1,461,214,441. This can be done by raising 1,461,214,441 to the power of 1/5:
1,461,214,441^(1/5) ≈ 50.66
Now substitute this value back into the original formula to calculate the lung volume for the Camel:
V ≈ 170 * 50.66 ≈ 8,623.22 milliliters
Therefore, the lung volume of the Camel is approximately 8,623.22 milliliters.
To find the lung volume of each mammal using the given model V = 170m^(4/5), we can substitute the given body mass (m) values into the formula and evaluate.
For the Mongoose with a body mass of 1.14 kg:
V = 170 * (1.14)^(4/5)
To evaluate this expression, we first need to calculate the 4/5th power of 1.14. To do this, we can use nth roots.
Step 1: Take the 4th root of 1.14 using a calculator:
1.14^(1/4) ≈ 1.0653
Step 2: Raise the result to the power of 5 using a calculator:
1.0653^5 ≈ 1.8013
Step 3: Substitute the value back into the original formula to find the lung volume:
V = 170 * 1.8013 ≈ 306.2218 milliliters
Therefore, the lung volume of the Mongoose is approximately 306.2218 milliliters.
Now let's calculate the lung volume for the Camel with a body mass of 229 kg:
V = 170 * (229)^(4/5)
Step 1: Take the 4th root of 229:
229^(1/4) ≈ 5.3278
Step 2: Raise the result to the power of 5:
5.3278^5 ≈ 1523.78
Step 3: Substitute the value back into the formula:
V ≈ 170 * 1523.78 ≈ 259465.6 milliliters
Therefore, the lung volume of the Camel is approximately 259465.6 milliliters.
you have the formula; plug in the number:
V(1.14) = 170 * 1.14^4/5
If you need to use nth roots, 1.14^4/5 = (1.14^1/5)^4 because n^1/5 is the 5th root
1.14^1/5 = 1.02655
1.02655^4 = 1.1105
as a check: 1.16^0.8 = 1.1105
So, V(1.14) = 170 * 1.1105 = 188.785