13.11.2022

# The half-life of gold-195m is approximately 30.5 seconds. Step 1 of 3 : Determine a so that A(t)=A0at describes the amount of gold-195m left after t seconds, where A0 is the amount at time t=0 . Round to six decimal places.

2

28.04.2023, solved by verified expert

0.977530

Step-by-step explanation:

The formula for radioactive decay is given by:

A(t) = A0 * e^(-kt)

where A0 is the initial amount of the radioactive substance, A(t) is the amount remaining after time t, k is the decay constant, and e is the base of the natural logarithm.

The half-life of gold-195m is given as t1/2 = 30.5 seconds. We know that after one half-life, the amount of the substance remaining is halved, so we can write:

A(t1/2) = A0 / 2

Substituting these values into the decay equation gives:

A(t1/2) = A0 * e^(-k*t1/2) = A0 / 2

Taking the natural logarithm of both sides gives:

ln(A0 / 2) = -k*t1/2

Solving for k, we get:

k = ln(2) / t1/2

Substituting this value of k back into the decay equation gives:

A(t) = A0 * e^(-ln(2)/t1/2 * t)

Simplifying this expression gives:

A(t) = A0 * (1/2)^(t/t1/2)

Therefore, we can see that a = (1/2)^(1/t1/2) = (1/2)^(1/30.5) which is approximately equal to 0.977530156. Rounded to six decimal places, a is 0.977530.

### Faq

Mathematics

Cost of 7 gallons=\$24.50

Cost of 1 gallon=24.50/7=3.5

Cost of 15 gallons=15*3.5=52.5

Cost of 15 gallons will be \$52.5

Mathematics

For 1 flavor there are 9 topping

Therefore, for 5 different flavors there will be 5*9 choices

No of choices= 5*9

=45

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The answer is in the image

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The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

Mathematics

The answer is in the image

Mathematics

tip=18% of 75.45

=18/100 * 75.45 = \$13.581

Tip = \$13.581

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