MATHEMATICS HIGH SCHOOL

Carbon-14 is a radioactive isotope that has a half-life of 5,730 years. Approximately how many years will it take for carbon-14 to decay to 10 percent of its original amount?

Answers

Answer 1

Answer:

Answer:

Carbon-14 will take 19,035 years to decay to 10 percent.

Step-by-step explanation:

Exponential Decay Function

A radioactive half-life refers to the amount of time it takes for half of the original isotope to decay.

An exponential decay can be described by the following formula:

$N(t)=N_(0)e^(-\lambda t)$

Where:

No = The quantity of the substance that will decay.

N(t) = The quantity that still remains and has not yet decayed after a time t

$\lambda$ = The decay constant.

One important parameter related to radioactive decay is the half-life:

$\displaystyle t_(1/2)=\frac {\ln(2)}{\lambda }$

If we know the value of the half-life, we can calculate the decay constant:

$\displaystyle \lambda=\frac {\ln(2)}{ t_(1/2)}$

Carbon-14 has a half-life of 5,730 years, thus:

$\displaystyle \lambda=\frac {\ln(2)}{ 5,730}$

$\lambda=0.00012097$

The equation of the remaining quantity of Carbon-14 is:

$N(t)=N_(0)e^(-0.00012097\cdot t)$

We need to calculate the time required for the original amout to reach 10%, thus N(t)=0.10No

$0.10N_o=N_(0)e^(-0.00012097\cdot t)$

Simplifying:

$0.10=e^(-0.00012097\cdot t)$

Taking logarithms:

$ln 0.10=-0.00012097\cdot t$

Solving for t:

$\displaystyle t=(log 0.10)/(-0.00012097)$

$t\approx 19,035\ years$

Carbon-14 will take 19,035 years to decay to 10 percent.

Answer 2

Answer:

Approximately 23,083 years will pass for carbon-14 to decay to 10 percent of its original amount.

To find out how long it will take for carbon-14 to decay to 10 percent of its original amount, we can use the concept of exponential decay. The formula for calculating the amount of a radioactive substance remaining after a certain time can be expressed as:

A(t) = A₀ * (1/2)ˣ/ₓ₂

Where:

A(t) is the amount of carbon-14 at time t

A₀ is the initial amount of carbon-14

t₁/₂ is the half-life of carbon-14 (5,730 years)

t is the time we want to find (in years)

We want to find t when A(t) is equal to 0.10 * A₀ (10 percent of the original amount). So, the equation becomes:

0.10 * A₀ = A₀ * (1/2)ˣ/₅₇₃₀

Now, we can cancel out A₀ on both sides of the equation:

0.10 = (1/2)ˣ/₅₇₃₀

To isolate t, we can take the logarithm of both sides (base 2) since the half-life is used in the equation:

log₂(0.10) = t / 5730

Now, we can solve for t:

t = 5730 * log₂(0.10)

To know more about decay here

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If m∠ABC = 72°, what is m∠DAB?

Answers

Value of ∠DAB is 108°

Intersection of Parallel lines:

Given that;

∠ABC = 72°

Find:

Value of ∠DAB

Computation:

We know that Line AD is parallel to line CB

So,

∠ABC + ∠DAB = 180°

72° + ∠DAB = 180°

∠DAB = 108°

Find out more information about 'Parallel line'

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Answer: m∠DAB=72

Step-by-step explanation:

Since we have given that

∠ABC = 72°

Since the lines AD and BC are parallel to each other,

As we know that when the two parallel lines cut by a transversal then the corresponding angles will be formed.

And the corresponding angles will be equal.

So, m∠ABC =m∠DAB=72°

Hence, m∠DAB=72°

How many solutions will the following equation have: x squared -49=0

Answers

Xsquere-49=0
Xsquere=49
X=√49 (squere root of 49 is 7)
i.e X=7

If u use factoring then x can be 7 or -7

Quadratic formula 2x²+9x-4=0

Answers

$2x^2+9x-4=0 \n \na=2 , b =9 , \ c=- 4 \n \n\Delta = b^(2)-4ac = 9^(2)-4*2* (- 4)= 81+32 =113 \n \nx_(1)=(-b-√(\Delta ))/(2a) =(-9- √(113))/(4) \n\nx_(2)=(-b+√(\Delta ))/(2a) = (-9+√(113))/(4)$

$2x^2+9x-4=0\ \ \ \ /:2\n\nx^2+(9)/(2)x-2=0\n\nx^2+2x\cdot(9)/(4)+((9)/(4))^2-((9)/(4))^2=2\n\n(x+(9)/(4))^2-(81)/(16)=2\n\n(x+(9)/(4))^2=(32)/(16)+(81)/(16)\n\n(x+(9)/(4))^2=(113)/(16)\iff x+(9)/(4)=-\sqrt(113)/(16)\ \vee\ x+(9)/(4)=\sqrt(113)/(16)\n\nx=-(9)/(4)-(√(113))/(4)\ \vee\ x=-(9)/(4)+(√(113))/(4)\n\nx=-(9+√(113))/(4)\ \vee\ x=-(9-√(113))/(4)$

I suck at math so I need help :(

Answers

This one is common sense, not math. You can't possibly get a 5 and a green face on the same roll, because all of the odd numbers are red. Each condition rules out the other one. That's called being "mutually exclusive".

shella is participating in a multi-day bike trip. on the first day, she rode 100 miles in 8 hours. use the expression d/t where d is the distance traveled and t is the travel time to find her average rate of travel. include units when evaluating the expression.

Answers

To solve this problem, first we have to substitute our integers in for our variables in the equation we are using.

d/t= 100 miles/8 hours

Then, we have to simplify the integer equation.

100 miles/8 hours = 12.5 miles per hour

This means that Shella traveled at an average speed of 12.5 mph on her bike trip.

The slope of the graph of y = x is

Answers

Hello,
y=1*x
Slope=1
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