3 years ago

Round this number the nearest hundredth 7.349

Mathematics

1 answer:

rusak2 [61]3 years ago

6 0

Answer:

Step-by-step explanation:

It is 7.3

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Explanation:

$\sf Half \ Life : A = A_O \ x \ (\dfrac{1}{2} )^{\dfrac{t}{h} }$

where A is final amount, Ao is initial amount, t is time taken, h is half life

Here given:

initial amount: 400 millicuries

final amount: 3.125 millicuries

half life: 8 days

time taken: ?

Hence solve for time taken:

$\sf \rightarrow A = A_O \ x \ (\dfrac{1}{2} )^{\dfrac{t}{h} }$

insert values given

$\sf \rightarrow 3.125 = 400 \ x \ (\dfrac{1}{2} )^{\dfrac{t}{8} }$

divide both sides by 400

$\sf \rightarrow (\dfrac{1}{2})^{\dfrac{t}{8}}=0.0078125$

apply exponent rule

$\sf \rightarrow {\dfrac{t}{8}}=\dfrac{ln(0.0078125)}{ln(1/2)}$

simplify

$\rightarrow \sf \dfrac{t}{8}=7$

multiply both sides by 8

$\rightarrow \sf t = 56$

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Step-by-step explanation:

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