To solve this we are going to use the half life equation

Where:

is the initial sample

is the time in years

is the half life of the substance

is the remainder quantity after

years
From the problem we know that:



Lets replace those values in our equation to find

:




We can conclude that after 1600 years of radioactive decay, the mass of the 100-gram sample will be
91.7 grams.
Total area = 104+24 = 128 sq.in , Option C is the right answer.
The missing figure is attached with the answer.
<h3>What is Area ?</h3>
The space occupied by a two dimensional figure is called Area.
The figure given in the question can be divided into two figure
A rectangle of 8 * 13 inch
and a triangle of 8 * 6 inch
The area of a rectangle is given by
Length * Breadth
8 * 13
= 104 sq.inch
The area of the triangle is given by
(1/2) * base * height
= (1/2) * 8 * 6
= 24 sq.inch
Total area = 104+24 = 128 sq.in
Therefore Option C is the right answer.
To know more about Area
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In the equation

divide both sides by
to get

Take the base-3/2 logarithm of both sides:

Alternatively, you can divide both sides by
:

Then take the base-2/3 logarith of both sides to get

(Both answers are equivalent)
Angle BAC is 45 degrees. The diagonal bisects angle BAD and since all angles in a square are 90 degrees, half of 90 is 45 degrees.