If 2a-b:2a+b=1:2find the value of a:b
1 answer:
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Answer:
a. The critcal points are at
b. Then, is a maximum and
is a minimum
c. The absolute minimum is at and the absolute maximum is at
Step-by-step explanation:
(a)
Remember that you need to find the points where
Therefore you have to solve this equation.
From that equation you can factor out and you would get
And from that you would have , so
.
And you would also have .
You can factor that equation as
Therefore .
So the critcal points are at
b.
Remember that a function has a maximum at a critical point if the second derivative at that point is negative. Since
Then, is a maximum and
is a minimum
c.
The absolute minimum is at and the absolute maximum is at
Answer:
a.
b. The value of stereo system after 2 years will be $628.23.
c. After approximately 4.98 years the stereo will be worth half the original value.
Step-by-step explanation:
Let x be the number of years.
We have been given that you purchased a stereo system for $830. The value of the stereo system decreases 13% each year.
a. Since we know that an exponential function is in form: , where,
a = Initial value,
b = For decay b is in form (1-r), where r is rate in decimal form.
Let us convert our given rate in decimal form.
Upon substituting our given values in exponential decay function we will get
Therefore, the exponential model represents the value of the stereo system in terms of the number of years since the purchase.
b. To find the value of stereo system after 2 years we will substitute x=2 in our model.
Therefore, the value of stereo system after 2 years will be $628.23.
c. The half of the original price will be .
Let us substitute y=415 in our model to find the time it will take the stereo to be worth half the original value.
Upon dividing both sides of our equation by 830 we will get,
Let us take natural log of both sides of our equation.
Using natural log property we will get,
Therefore, after approximately 4.98 years the stereo will be worth half the original value.