Answer:
[tex]\huge\boxed{576 \ \text{calories}}[/tex]
Step-by-step explanation:
In order to find the number of calories that an [tex]m[/tex] kg animal weighs, we can substitute what we need inside the formula given, [tex]72m^{\frac{3}{4}}[/tex]. Since we want to find how much a 16 kg dog needs to eat, we substitute 16 in as m.
[tex]72\cdot 16^{\frac{3}{4}}[/tex]
BPEMDAS tells us that the order of solving equations is
Brackets
Parantheses
Exponents
Multiplication/Division
Addition/Subtraction
Looking at this order, we need to do [tex]16^{\frac{3}{4}}[/tex], then multiply by 72.
When we have a number to a fraction power, we need to note that
- It's the same as taking the denominator root of the base to the numerator power
Therefore, our expression will be [tex]\sqrt[4]{16^3}[/tex].
- [tex]16^3 = 4096[/tex]
- [tex]\sqrt[4]{4096} = 8[/tex]
Now that we have this much, we need to multiply it by 72 as our formula read [tex]72m^{\frac{3}{4}}[/tex].
- [tex]72 \cdot 8=576[/tex]
Therefore, an animal weighing 16 kg needs to consume 576 calories.
Hope this helped!
