Which exponential function goes through the points (1, 16) and (4, 128)?
1 answer:
Answer:
Here is the complete question (attachment).
The function which represent the given points are
Step-by-step explanation:
We know that a general exponential function is like,
We can find the answer by hit and trial method by plugging the values of coordinates.
Here we are going to solve this with the above general formula.
So as the points are then for
Can be arranged in terms of the general equation.
...equation(1) and
...equation(2)
Plugging the values in equation 2.
We have
Plugging in equation 1.
We have
Comparing with the general equation of exponential and
So the function which depicts the above points =
From theoption we have B as the correct answer.
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We call:
T = Tom's paiting rate
G = George's paiting rate
M = Mario's paiting rate
As the first statement says that they can work together, then:
T + G + M = Painting rate working together, that is the surface area they paint per hour.
Since the problem says that they last four hours painting a
room, then we need to multiply the amount of hours times the painting rate that is equal the surface area of the room, so:
4(T + G + M) = 600
Applying a similar reasoning, the George and Mario's painting rate is:
0 + G + M
Note that 0 implies that Tom didn't work in this case.
As they last eight hours painting the room, then:
8(0 + G + M) = 600
The same reasoning is applied to Tom and George working together. In this case 0 implies that Mario didn't work, so:
6(T + G + 0) = 600
We have a system of linear equations in three variables T, G, M:
<span>4(T+G+M)=600
8(0+G+M)=600
6(T+G+0)=600
</span>
Solving:
(1) T + G + M = 150
(2) G + M = 75
(3) T + G = 100
Substitute (3) in (1):
100 + M = 150 ∴ M = 50
Replace M in (2):
G + 50 = 75 ∴ G = 25
Substitute G in (3)
T + 25 = 100 ∴ T = 75
Then, the painting rates are:
Tom = 75
George = 25
Mario = 50
<span>Solving for Time to determine how long it would take Tom to paint the room alone:
</span>
<span>Painted Area = Painting Rate×Time, so:
</span>
T = Tom's paiting rate
G = George's paiting rate
M = Mario's paiting rate
As the first statement says that they can work together, then:
T + G + M = Painting rate working together, that is the surface area they paint per hour.
Since the problem says that they last four hours painting a
4(T + G + M) = 600
Applying a similar reasoning, the George and Mario's painting rate is:
0 + G + M
Note that 0 implies that Tom didn't work in this case.
As they last eight hours painting the room, then:
8(0 + G + M) = 600
The same reasoning is applied to Tom and George working together. In this case 0 implies that Mario didn't work, so:
6(T + G + 0) = 600
We have a system of linear equations in three variables T, G, M:
<span>4(T+G+M)=600
8(0+G+M)=600
6(T+G+0)=600
</span>
Solving:
(1) T + G + M = 150
(2) G + M = 75
(3) T + G = 100
Substitute (3) in (1):
100 + M = 150 ∴ M = 50
Replace M in (2):
G + 50 = 75 ∴ G = 25
Substitute G in (3)
T + 25 = 100 ∴ T = 75
Then, the painting rates are:
Tom = 75
George = 25
Mario = 50
<span>Solving for Time to determine how long it would take Tom to paint the room alone:
</span>
<span>Painted Area = Painting Rate×Time, so:
</span>