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3 years ago

Element X decays radioactively with a half life of 8 minutes. If there are 480 grams of

Mathematics

1 answer:

Vaselesa [24]3 years ago

6 0

Answer:

40.8 minutes

Step-by-step explanation:

Element X decays radioactively with a half life of 8 minutes. If there are 480 grams of Element X, how long, to the nearest tenth of a minute, would it take the element to decay to 14 grams?

The formula to find how long it would take which is the time elapsed is given as:

t = t½ × In(Nt/No)/-In2

t = ?

t½ = 8 minutes

Nt = Amount after the time of decay = 14 grams

No = Original Amount of substances = 480 grams

t = 8 × In(14/480)/-In2

t = 40.796285388407 minutes

Approximately to the nearest tenth = 40.8 minutes

Therefore, it would take the element X, 40.8 minutes to decay to 14 grams

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An equation is an expression that shows the relationship between two or more variables and numbers.

Given that:

$a_n=1 + (-\frac{4}{9} )^n\\\\When\ n=1:a_1=1 + (-\frac{4}{9} )^1=0.5556\\\\When\ n=2:a_2=1 + (-\frac{4}{9} )^2=1.1975\\\\When\ n=3:a_3=1 + (-\frac{4}{9} )^3=0.9122\\\\When\ n=4:a_4=1 + (-\frac{4}{9} )^4=1.039\\\\When\ n=5:a_5=1 + (-\frac{4}{9} )^5=0.9827\\\\When\ n=6:a_6=1 + (-\frac{4}{9} )^6=1.0077\\\\When\ n=7:a_7=1 + (-\frac{4}{9} )^7=0.9966\\\\When\ n=8:a_8=1 + (-\frac{4}{9} )^8=1.0015\\\\When\ n=9:a_9=1 + (-\frac{4}{9} )^9=0.9993\\\\$

$When\ n=10:a_{10}=1 + (-\frac{4}{9} )^{10}=1.0003\\$

The first ten terms of the sequence $a_n=1 + (-\frac{4}{9} )^n$ is<em> 0.5556, 1.1975, 0.9122, 1.039, 0.9827, 1.0077, 0.9966, 1.0015, 0.9993 and 1.0003</em>

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