Which recursive formula can be used to generate the sequence below, where f(1) = 3 and n ≥ 1?
2 answers:
Answer:
, where f(1)=3
Step-by-step explanation:
The given sequence is; 3, –6, 12, –24, 48, …
The first term of this sequence is
There is a common ratio of
We can actually use any other two consecutive terms in the sequence to obtain the common ratio.
The recursive formula is given by:
We plug in the common ratio to get:
, where f(1)=3
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Answer:
Carbon-14 loses around 10% ( 0.1 in decimal form) of its mass, after one millennium.
Then if we start with a mass A of Carbon-14, after one millennium we will have a mass equal to:
A - A*0.1 = A*(0.9)
After another millennium, we will have a mass equal to:
A*(0.9) - A*(0.9)*0.1 = A*(0.9)^2
And so on, this is an exponential decay.
We already can see the pattern here, after x millenniums, the mass of carbon-14 will be:
M(x) = A*(0.9)^x
Now, in this problem we have 600 grams of carbon-14, then the equation for the mass will be:
y = M(x) = 600g*(0.9)^x
And the graph of this equation is shown below.
