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Here are a few recommended readings before getting started with this lesson.
After becoming a subscriber of a streaming platform, Magdalena became interested in a particular crime series. While watching an episode, she found out that after an accident, police can determine the speed of a car before the driver started braking.
The speed of a car can be estimated by using the following formula.Magdalena shared her streaming account with Kriz so that they can watch a new nature documentary. The documentary is about the work of a Swiss agricultural biologist, Max Kleiber. He researched how the mass of an animal influences the animal's metabolic rate.
Metabolic Rate |
The rate at which a person or an animal burns calories to maintain its body weight. |
Mammal | Mass |
---|---|
Mouse | 20 g |
Kriz | 81 kg |
Horse | 625 kg |
Mammal | Mass (kg) | Metabolic Rate (kcal/day) |
---|---|---|
Mouse | 0.02 | ≈3.72 |
Kriz | 81 | 1890 |
Horse | 625 | 8750 |
Multiply
LHS/70=RHS/70
LHS4=RHS4
(ab)m=ambm
(na)n=a
3LHS=3RHS
3a⋅b=3a⋅3b
3a3=a
na=an1
(am)n=(an)m
an1=na
Calculate root
Calculate power and product
LHS⋅32=RHS⋅32
32⋅32a=a
Identity Property of Multiplication
LHS−v=RHS−v
Rearrange equation
LHS2=RHS2
(a)2=a
Distribute 64
(a−b)2=a2−2ab+b2
LHS−v2=RHS−v2
(ab)m=ambm
Calculate power and product
LHS−64s=RHS−64s
LHS/(-64)=RHS/(-64)
Distribute -641
t=1
1a=1
Identity Property of Multiplication
Add terms
Next, the second equation y=2t−16 will be graphed in the same coordinate plane by using a table of values. Remember to substitute t≥8 so that the square root can be calculated right away.
t | 2t−16 | y=2t−16 |
---|---|---|
8 | 2(8)−16 | 0=0 |
10 | 2(10)−16 | 4=2 |
16 | 2(16)−16 | 16=4 |
26 | 2(26)−16 | 36=6 |
40 | 2(40)−16 | 64=8 |
58 | 2(58)−16 | 100=10 |
All these points will be plotted and connected with a smooth curve.
According to the graph, Magdalena ran the first 2 kilometers in 10 minutes, while Kriz ran the first 2 kilometers in 2 minutes. They met 10 minutes from the start of the marathon. After this time, Kriz was in front of Magdalena for a while.