Question

Sodium-24 has an hourly decay rate of about 5%. How many grams of a 900 g sample will remain after 90 hours? Round the answer to two decimal places.
7.03 g
7.50 g
8.90 g
28.13 g

Answer 1

Answer:

The answer is 8.90g If this helped you in any way pls mark this answer as brainliest pls.

Step-by-step explanation:

Answer 2

900 g of sample of Sodium-24 will remain after 90 hours at the decay rate of 5% is equals to 8.90 grams.

What is decay rate?

" Decay rate is defined as the quantity get decays at the rate of  proportional to given quantity as per the given conditions."

Formula used

$y = a ( 1-r )^{n}$

y = amount left after decay

a = given quantity

r = rate of decay

n = time

According to the question,

Given values,

Sample quantity = 900 grams

Decay rate = 5%

Time = 90 hours

Substitute the value in the formula to get the quantity after decay rate,

$y = 900( 1- \frac{5}{100} )^{90} \\\\\implies y = 900(95)^{90}$

Take log both the side we get,

$log y = log900 + 90log95\\\\\implies logy = 2.9542 + 90(1.9777)\\\\\implies logy = 180.9472\\\\\implies y = antilog (180.9472)\\\\\implies y = 8.855$

y = 8.90 grams (round up to two decimal places)

Hence, 900 g of sample of Sodium-24 will remain after 90 hours at the decay rate of 5% is equals to 8.90 grams.

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