Ancient paintings were found on cave walls in south america. the carbon-14 in the paintings was measured and was found to be 19% of the original weight. how old were the paintings?
a. 3,839
b. 9,239
c. 13,839
d. 19,239

C. 13,839 (the answer is not among the given options, however the result is near this value)

Step-by-step explanation:

The exponential decay model for Carbon- 14 is given by the followig formula:

 (1)

Where:

is the final amount of Carbon- 14  

is the initial amount of Carbon- 14

is the time elapsed (the value we want to find)

On the other hand, we are told the current amount of Carbon-14  is , assuming the initial amount of Carbon-14 is  :

(2)

This means: (2)

Now,finding from (1):

 (3)

Applying natural logarithm on both sides:

 (4)

 (5)

 (6)

Finally:

 This is the age of the paintings and the option that is nearest to this value is C. 13839 years

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation:

i think the answer is true

step-by-step explanation: