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aimee80
29.07.2019 •
Mathematics
Robin bought a computer for $1,250. it will depreciate, or decrease in value, by 10% each year that she owns it. a) is the sequence formed by the value at the beginning of each year arithmetic, geometric, or neither? explain. b) write an explicit formula to represent the sequence. c) find the value of the computer at the beginning of the 6th year.
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Ответ:
where
Also, to find
where
a) Lets find the three first terms of our sequence to check what type of sequence we have:
We know for our problem that the initial value of the computer is $1250, so our first term is 1250. In other words
To fin our second term
To find our third term
Now that we have our sequence
- with
- with
Look! our
b) To do this we just need to replece the values of our sequence in the general formula of a geometric sequence. We know from our previous point that
c) To find the value of the computer at the beginning of the 6th year, we just need to find the 6th therm in our geometric sequence:
We can conclude that the value of the computer at the beginning of the 6th year will be $738.1125
Ответ:
We want to answer different things about an exponential decay, the answers are:
a) Geometric.b)So we know that the original price of the computer is $1250 and the value decays by 10% each year.
So in year 1, the new value of the computer will be:
V = $1250*(1 - 0.1) = $1250*0.9
On year 2, the new value will be:
V = ( $1250*0.9)*0.9 = $1250*(0.9)^2
And so on.
a) This sequence is a geometric sequence because each term is a constant times the previous term, where the constant is 0.9.
b) The explicit formula for a geometric sequence is:
where:
k is the constant, in this case, is 0.9
A1 is the first term of the sequence, in this case, is 1250
Then we have:
c) Here we just need to replace n by 6 in the above formula:
This means that the price of the computer in the 6th year is $738.10
If you want to learn more about exponential decays, you can read:
link
Ответ:
94
Step-by-step explanation: