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8090 [49]
10 months ago
10

Situation:A researcher in North America discoversa fossile that contains 65% of its originalamount of C-14..-ktN=NoeNo inital am

ount of C-14 (at time=t = 0)N== amount of C-14 at time tk= 0.0001t = time, in yearsFind the age of the fossile to the nearest year.
Mathematics
1 answer:
zheka24 [161]10 months ago
8 0

SOLUTION

We have been given the equation of the decay as

\begin{gathered} N=N_0e^{-kt} \\ where\text{ } \\ N_0=initial\text{ amount of C-14 at time t} \\ N=amount\text{ of C-14 at time t = 65\% of N}_0=0.65N_0 \\ k=0.0001 \\ t=time\text{ in years = ?} \end{gathered}

So we are looking for the time

Plugging the values into the equation, we have

\begin{gathered} N=N_0e^{-kt} \\ 0.65N_0=N_0e^{-0.0001t} \\ e^{-0.0001t}=\frac{0.65N_0}{N_0} \\ e^{-0.0001t}=0.65 \end{gathered}

Taking Ln of both sides, we have

\begin{gathered} ln(e^{-0.000t})=ln(0.65) \\ -0.0001t=ln(0.65) \\ t=\frac{ln(0.65)}{-0.0001} \\ t=4307.82916 \end{gathered}

Hence the answer is 4308 to the nearest year

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Write<br> 9/18<br> in lowest terms
kogti [31]

Answer:

1/2

Step-by-step explanation:

7 0
3 years ago
Hannah earned $1536 in 8 years on an investment at a 4% annual simple interest rate. How much was Hannah’s investment? $4800 $30
Nonamiya [84]

Simple interest calculates interest on initial amount only. The investment by Hannah was : Option A: $4800

<h3>How to calculate simple interest amount if rate of interest is R% annually?</h3>

Suppose that the initial amount of investment is P

And the rate of simple interest is R% annually,

And the time of investment is T years.

Then, the amount of simple interest is calculated as:

I = \dfrac{P \times R \times T}{100}

For the given case, let the initial investment Hannah made was of $P

Then, the time of investment is T = 8 years, R% = 4%, and given that Hannah earned interest I = $1536

Putting values in the above formula, we get;

I = \dfrac{P \times R \times T}{100}\\\\1536 = \dfrac{P \times 8 \times 4}{100}\\\\P = \dfrac{153600}{32} = 4800

Thus,

The investment by Hannah was : Option A: $4800

Learn more about simple interest here:

brainly.com/question/5319581

5 0
2 years ago
Which number is located at Point A on the number line?<br> –4 my answer<br> 4<br> –6<br> 6
OLEGan [10]

Answer:

-6

Step-by-step explanation:

you have to look at the numbers next to it

7 0
3 years ago
Solve the following quadratics. State the FACTORS AND SOLUTIONS. 1. 2x^2 - 7x + 3 2. 3x^2 + 7x +2
tekilochka [14]

Answer:

1. x = 3, 1/2 (solutions); (x - 3)(2x - 1) (factors)

2. x = -1/3, -2 (solutions); (3x + 1)(x + 2) (factors)

Step-by-step explanation:

<u>1. 2x^2 - 7x + 3</u>

To solve problem 1, you will need to identify your a, b, and c values in this quadratic function.

Since this problem is in standard form, it will be easy to identify these values. The standard form of a quadratic function is ax^2 + bx + c.

The a value is 2, the b value is -7, and the c value is 3 if we use our standard form and see which numbers are plugged into it.

Since we know that

  • a = 2
  • b = -7
  • c = 3

we can use the quadratic formula: x = \frac{-b~\pm~\sqrt{b^2~-~4ac} }{2a}

Substitute the a, b, and c values into the quadratic formula: x=\frac{-(-7)\pm\sqrt{(-7)^2-4(2)(3)} }{2(2)}

Now simplify using the laws of pemdas: x=\frac{7\pm\sqrt{(49)-(24)} }{4}

Simplify even further: x=\frac{7\pm\sqrt{(25)} }{4} \rightarrow x=\frac{7\pm (5) }{4}

Now split this equation into two equations to solve for x: x=\frac{12 }{4} ~~and~~ x=\frac{2 }{4}

12/4 can be simplified to 3, and 2/4 can be simplified to 1/2.

This means your solutions to problem 1 is 3, 1/2.

\boxed {x=3,\frac{1}{2} }

There is also another way to solve for the quadratic functions, and this was by factoring.

If you factor 2x^2 - 7x + 3 using the bottoms-up method, you will get (x - 3)(2x - 1).

After factoring, solving for the solutions is simple because all you have to do is set each factor to 0.

  • x - 3 = 0
  • 2x - 1 = 0

After solving for x by adding 3 to both sides, or by adding 1 to both sides then dividing by 2, you will end up with the same solutions: x = 3 and x = 1/2.

<u>2. 3x^2 + 7x + 2</u>

To save time I'll be using the bottoms-up factoring method, but remember to refer back to problem 1 (quadratic formula) if you prefer that method.

Factor this quadratic function using the bottoms-up method. After factoring you will have (3x + 1)(x + 2). These are your factors.

Now to solve for x and find the solutions of the quadratic function, you will set both factors equal to 0.

  • 3x + 1 = 0
  • x + 2 = 0

Solve.

<u>First factor:</u> 3x + 1 = 0

Subtract 1 from both sides.

3x = -1

Divide both sides by 3.

x = -1/3

<u>Second factor:</u> x + 2 = 0

Subtract 2 from both sides.

x = -2

Your solutions are x = -1/3 and x = -2.

\boxed {x = -\frac{1}{3} , -2}

7 0
3 years ago
Jim spins a spinner with colors red, blue, yellow, purple, green, and orange. Jim also flips a coin. What is the probability tha
S_A_V [24]
Probability=number of specific outcomes/total possible outcomes

And the probability of two events happening at the same time is P(1)*P(2), or the product of the probabilities of each event...

In this case:

P(primary color)=3/6=1/2

P(head)=1/2

P(primary and head)=(1/2)(1/2)=1/4
4 0
3 years ago
Read 2 more answers
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