Sergio consumes an energy drink that contains caffeine. After consuming the energy drink, the amount of caffeine in Sergio's body decreases exponentially. The 10-hour decay factor for the number of mg of caffeine in Sergio's body is 0.2661.
What is the 5-Hour growth/decay factor for the number of mg of caffeine in Eric's body?

0.5158

Step-by-step explanation:

The exponential decay of a given material is used to describe the process by which a material decreases in size and amount over a specific period of time. The material will decay with respect to its decay factor. Therefore, if the 10-hour decay factor is approximately 0.2661, the 5-hour growth/decay factor will be: (0.2661)^(5/10) = (0.2661)^0.5 = 0.5158.

0.5158

Step-by-step explanation:

Given, 10 hour Sergio's decay factor = 0.2661

First calculate for 1 hour decay factor

1 hour decay factor = (10 hour decay factor)^1/10

= (0.2661)^1/10

1 hour decay factor = 0.8760

Therefore to calculate for 5 hour decay factor

5 hour decay factor = (1 hour decay factor)^5

= (0.8760)^5

= 0.5158

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584