1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Lemur [1.5K]
3 years ago
13

The ratio of 14C to 12C in living organisms is 1.3 × 10-12. The fossilized remains of an organism are discovered and the ratio o

f 14C to 12C in the fossil is measured to be 4.6 × 10-13. How long ago, in years was the organism alive? (The half life of 14C is 5,730 years.)
Mathematics
1 answer:
soldi70 [24.7K]3 years ago
8 0

Answer:

t = 8588 years

Step-by-step explanation:

From the given information:

Using the formula:

k = \dfrac{In (2)}{t_{1/2}}

Given that:

t_{1/2} = 5730 years

Then:

k = \dfrac{In (2)}{5730}

k = \dfrac{0.6931472}{5730}

k = 1.20968 × 10⁻⁴

However; the expression to find the value of x is:

x= x_oe^{-kt}

4.6 \times 10^{-13} = 1.3 \times 10^{-12} \times e^{(-1.20968\times 10^{-4} \times t)}

\dfrac{4.6 \times 10^{-13} }{1.3 \times 10^{-12}}=  e^{(-1.20968\times 10^{-4} \times t)}

0.353846=  e^{(-1.20968\times 10^{-4} \times t)}

(-1.20968 × 10⁻⁴ × t) = In(0.353846)

(-1.20968 × 10⁻⁴ × t) = -1.03889

t = \dfrac{-1.03889}{-1.20968 \times 10^{-4}}

t = 8588 years

You might be interested in
Mary spends no more than 21 hours a week doing homework. If she spends 2/7 of the time doing her math homework, what other fract
True [87]

Answer:

6/21, 12/42

Step-by-step explanation:

Mary spends no more than 21 hours a week doing homework. If she spends 2/7 of the time doing her math homework.

The number of hours she spends doing her maths homework is calculated as:

= 2/7 × 21

= 6 hours

The other fractions that could represent the amount of time Mary spends doing her math homework is given as:

6 hours/21 hours = 6/21

Also , that could be represented as:

12/42

Therefore, the other fractions that could represent the amount of time Mary spends doing her math homework is : 6/21 , 12/42

5 0
3 years ago
For the points in the table, does pressure vary directly with volume? If so, identify k and write an equation. No, this is not a
wel
Can't see the table but direct variation is: y = kx
So if the output is some constant multiple which could be positive, negative or fraction then yes it is direct variation. So just divide a couple y/x = k to see what you get.
7 0
3 years ago
Read 2 more answers
Find an explicit rule for the nth term of the sequence.The second and fifth terms of a geometric sequence are 18 and 144, respec
vova2212 [387]

Given:

second term = 18

fifth term = 144

The nth term of a geometric sequence is:

\begin{gathered} a_n\text{ = ar}^{n-1} \\ Where\text{ a is the first term} \\ r\text{ is the common ratio} \end{gathered}

Hence, we have:

\begin{gathered} \text{ar}^{2-1}\text{ = 18} \\ ar\text{ = 18} \\  \\ ar^{5-1}=\text{ 144} \\ ar^4\text{ =144} \end{gathered}

Divide the expression for the fifth term by the expression for the second term:

\begin{gathered} \frac{ar^4}{ar}\text{ = }\frac{144}{18} \\ r^3\text{ = }\frac{144}{18} \\ r\text{ = 2} \end{gathered}

Substituting the value of r into any of the expression:

\begin{gathered} ar\text{ =  18} \\ a\text{ }\times\text{ 2 =  18} \\ Divide\text{ both sides by 2} \\ \frac{2a}{2}\text{ =}\frac{18}{2} \\ a\text{ = 9} \end{gathered}

Hence, the explicit rule for the sequence is:

a_n\text{ = 9\lparen2\rparen}^{n-1}

5 0
1 year ago
WILL GIVE BRAINLIEST!
kvasek [131]
1.D, both.
not sure of the other though
6 0
3 years ago
Read 2 more answers
46 decreased by twice Chau's savings. use the variable c to represent Chau's savings.
dedylja [7]
46 -2c

46 decreased by means 46 minus
Twice c would be c times 2
4 0
3 years ago
Other questions:
  • If the following two triangles are similar, find X.<br><br> Show work please
    13·1 answer
  • The plot in A - D all show ________ correlation.
    9·2 answers
  • What is the equation that passes through (4, 3) and (2, -1)?
    8·2 answers
  • Makayla is taking a math course and is working with the perimeter of rectangles. She knows the perimeter and length of her recta
    9·2 answers
  • The superintendent of schools had all students in town vote on whether the schools should offer soup on the lunch menu. When the
    11·1 answer
  • What conversion factor is appropriate to express the cost of 5.3 lb of apples?
    12·1 answer
  • Can you answer all of these please thank you who ever is right will get a Brainliest tomorrow
    6·1 answer
  • Two lines intersect, and you know the measure of one angle. How can you determine the measures of the other three angles
    11·2 answers
  • yo i need help please no links i just need the answer to pass my exit ticket please i’ll give u a brainliest
    13·1 answer
  • Plzzzzzzz helppppppppppppp
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!