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Cerrena [4.2K]
3 years ago
13

Isotope X has a half-life of 8.00 minutes. How much of a 75.0 g sample will remain

Mathematics
1 answer:
Oksana_A [137]3 years ago
6 0

After 8.00 min, 75.0/2 = 37.5 g of the sample remains.

After another 8.00 min (total 16.0 min), 37.5/2 = 18.75 g remains. (Equivalently, 75.0/2^2 g)

After another 8.00 min (total 24.0 min), 18.75/2 = 9.375 g remains. (Or 75.0/2^3 g)

Finally, after another 8.00 min (total 32.0 min), 9.375/2 = 4.6875 g remains (or 75.0/2^4 g), approximately 4.69 g.

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Using the speed - distance relationship, the time left before the appointed time is 27 minutes.

<u>Recall</u><u> </u><u>:</u>

  • Distance = speed × time

  • Let time = t

<u>At</u><u> </u><u>10mph</u><u> </u><u>:</u>

  • Distance = 10 × (t + 3) = 10t + 30 - - - (1)

<u>At</u><u> </u><u>12</u><u> </u><u>mph</u><u> </u><u>:</u>

  • Distance = 12 × (t - 2) = 12t - 24 - - - - (2)

<em>Equate</em><em> </em><em>(</em><em>1</em><em>)</em><em> </em><em>and</em><em> </em><em>(</em><em>2</em><em>)</em><em> </em><em>:</em>

10t + 30 = 12t - 24

<em>Collect</em><em> </em><em>like</em><em> </em><em>terms</em><em> </em>

10t - 12t = - 24 - 30

-2t = - 54

<em>Divide</em><em> </em><em>both</em><em> </em><em>sides</em><em> </em><em>by</em><em> </em><em>-</em><em> </em><em>2</em>

t = 54 / 2

t = 27

Hence, the time left before the appointed time is 27 minutes.

Learn more : brainly.com/question/25669152

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Archy [21]

Answer:

The population will be 896 turtles 6 years later ⇒ B

Step-by-step explanation:

The exponential increasing formula is y = a(1+r)^{x}, where

  • y is the new value
  • a is the initial value
  • r is the rate of increase in decimal
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∵ There are 300 turtles

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∵ The population of the turtles exponentially increases 20% each year

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