An engineer wants to build a bridge across a gorge as shown in the figure above. To calculate the length the bridge will need to
1 answer:
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Answer:
One convergence criteria that is useful here is that, if aₙ is the n-th term of this sequence, then we must have:
Iaₙ₊₁I < IaₙI
This means that the absolute value of the terms must decrease as n increases.
Then we must have:
We can write this as:
If we assume that n is a really big number, then:
n + 1 ≈ 1
And we can write:
Then we have the inequality
And remember that this must be in absolute value, then we will have that:
-1 < (x - 2)/3 < 1
-3 < x - 2 < 3
-3 + 2 < x < 3 + 2
-1 < x < 5
The first option looks like this, but it uses the symbols ≤≥, so it is not the same as this, then the correct option will be the second.
Answer:
Present value = $4,122.4
Accumulated amount = $4,742
Step-by-step explanation:
Data provided in the question:
Amount at the Start of money flow = $1,000
Increase in amount is exponentially at the rate of 5% per year
Time = 4 years
Interest rate = 3.5% compounded continuously
Now,
Accumulated Value of the money flow =
The present value of the money flow =
=
=
=
= 1000 × [70.7891 - 66.6667]
= $4,122.4
Accumulated interest =
=
= $4,742