100 points
2 answers:
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<h2>Answer:</h2>
The correct options are:
- The domain is all real numbers.
- The base must be less than 1 and greater than 0.
- The function has a constant multiplicative rate of change.
We know that the exponential function is given by:
where a>0 and b are constants.
Also, it represents a growth function if b>1
and a decay function if 0<b<1
where b is the base.
- x belongs to whole of the real numbers( since the exponential function is well defined for all the real values of x.
Hence, the domain of the function is all the real numbers )
- Also, the graph of a decay function decreases continuously i.e. with the increasing input value the output value decreases.
- The exponential decay function always have a constant multiplicative rate of change i.e. b.
Complete Question
The complete question is shown on the first uploaded image
Answer:
The optimal point(i.e the position of P) that will allow Sally to reach the cabin as quickly as possible is from the cabin.
Step-by-step explanation:
From the question we are told that
The speed from the point Sally is standing to the point P is
The speed from the point P to the cabin is
Let denote the distance from the bottom left corner to the P be y ft
Generally according to Pythagoras theorem the distance from Sally's first position to point P is mathematically represented as
Generally the distance from that point P to the cabin is mathematically represented as
Generally the time it takes Sally to cover that distance s is mathematically represented as
=>
Generally the time it takes Sally to cover that distance d is mathematically represented as
=>
So the total time taken is
Generally the minimum time taken with respect to the distance is mathematically evaluated by differentiating and equating the derivative to 0
So
=>
=>
=>
=>
So the distance from point P to the cabin is
=>
So the optimal point(i.e the position of P) that will allow Sally to reach the cabin as quickly as possible is from the cabin
