<h2>
Answer: 816 years</h2>
This problem can be solved using the <u>Radioactive Half Life Formula:
</u>
<u />
(1)
Where:
is the final amount of the material
is the initial amount of the material
is the time elapsed (the quantity we are asked to find)
is the half life of americium-241
Knowing this, let's find from (1):
Applying natural logarithm in both sides:
<u></u>
<u>Finally:</u>
I would rather run a 100 mph
Recursive
formula is one way of solving an arithmetic sequence. It contains the initial
term of a sequence and the implementing rule that serve as a pattern in finding
the next terms. In the
problem given, the 6th term is provided, therefore we can solve for the initial
term in reverse. To make use of it, instead of multiplying 1.025, we should divide it after
deducting 50 (which supposedly is added).
<span>
Therefore, we perform the given formula: A (n) = <span>1.025(an-1) +
50
</span></span>a(5) =1.025 (235.62) + 50 = 291.51
a(4) = 1.025 (181.09) + 50 = 235.62
a(3) = 1.025 (127.89) + 50 = 181.09
a(2) = 1.025 (75.99) + 50 = 127.89
a(1) = 1.025 (25.36) + 50 = 75.99
a(n) = 25.36
The terms before a(6) are indicated above, since a(6) is already given.
So, the correct answer is <span>
A. $25.36, $75.99.</span>