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
Vikentia [17]
3 years ago
5

An Archaeologist in Turkey discovers a spear head that contains 51% of its original amount of C-14. Find the age of the spear he

ad to the nearest year.
Mathematics
2 answers:
Ne4ueva [31]3 years ago
5 0

Answer: 5566 years

Step-by-step explanation:

We know that the half-life of carbon-14 is 5730 years.

Let x be the original amount of C-14 , then the current amount of C-14 =0.51x

The radioactive half-life formula for C-14 is given by :-

P=P_0(0.5)^{\dfrac{t}{t_{\frac{1}{2}}}}, where P is the amount of C-14 at time t and  P_0 is the original amount.

\Rightarrow\ 0.51x=x(0.5)^{\dfrac{t}{5730}}\\\\\Rightarrow\ 0.51=(0.5)^{\dfrac{t}{5730}}

Taking log on both the sides , we get

\log(0.51)=\dfrac{t}{5730}\log(0.5)\\\\\Rightarrow\ -0.292429823902=\dfrac{t}{5730}\times-0.301029995664\\\\\Rightarrowt=\dfrac{5730\times0.292429823902}{0.301029995664}=5566.29875791\approx5566\text{years}

Hence, the age of the spear head is 5566 years.

disa [49]3 years ago
3 0
Use given half-life for C-14 of 5,730 years.

The exponential decay function:
y = e^{-kt}
plug in half life, solve for 'e^(-k)'
0.5 = e^{-5730k} \\  \\ 0.5 = (e^{-k})^{5730} \\  \\ e^{-k} = (0.5)^{1/5730}

Sub into original decay function, plug in 0.51 for 'y' and solve for 't'

y = e^{-kt} = (e^{-k})^t  \\  \\ 0.51 = (0.5)^{t/5730} \\  \\ ln(0.51) = \frac{t}{5730} ln(0.5) \\  \\ t = 5730 \frac{ln 0.51}{1n 0.5}
You might be interested in
Change 22 metres per second to a speed in kilometres per hour.<br> Show your working clearly.
masha68 [24]

Answer:

79.2 km/hour

Step-by-step explanation:

1 m/sec= 3.6 km/hour 22m/sec= ? so just multiply 22 m/sec by 3.6 km/hour then the answer will be :- 79.2 km/hour

7 0
3 years ago
How many times larger is a 10pound dog from a hamster weighing 5/8 pound
lutik1710 [3]
 it would be 16 times larger
6 0
3 years ago
1. Write the following in exponential form and as a multiplication sentence using only 10 as a factor
Irina-Kira [14]

Answer:

1. a. 1,000 = 10³ = 10 × 10 × 10

b. 100 × 100 = 10² × 10² = 10 × 10 × 10 × 10

2. a. 3 × 10² = 300

b. 2.16 × 10⁴ = 21,600

c. 800 ÷ 10³ = 0.8

d. 754.2 ÷ 10² = 7.542

Step-by-step explanation:

3. a. 1,000

There are 3 zeros in 1000. This is equivalent to 10 raised to the power of 3. Writing this in multiplication sentence using 19 as the only factor, we would have:

1,000 = 10³ = 10 × 10 × 10

b. 100 × 100

Using the same logic as explained in (a) above, we would have:

100 × 100 = 10² × 10² = 10 × 10 × 10 × 10

2. a. 3 × 10²

Convert 10² to 100 and multiply both numbers

3 × 10² = 3 × 10 × 10 = 3 × 100 = 300

b. 2.16 × 10⁴

2.16 × 10 × 10 × 10 × 10 = 2.16 × 10,000

Multiplying both numbers, since we have 4 zeros, move the decimal point 4 places to the right.

2.16 × 10,000 = 21,600

c. 800 ÷ 10³ = 800 ÷ 10 × 10 × 10

800 ÷ 1,000

There are 3 zeros in 1000, since we are dividing, move the decimal point 3 places to the left.

800 ÷ 1,000 = 0.8

d. 754.2 ÷ 10² = 754.2 ÷ 10 × 10

754.2 ÷ 100

Move the decimal point 2 places to the left.

754.2 ÷ 100 = 7.542

5 0
3 years ago
An ice cream truck began its daily route with 95 gallons of ice cream. The truck driver sold 78% of the
Brilliant_brown [7]

Answer:

74.1 or 74

Step-by-step explanation:

3 0
3 years ago
Help ASAP plz!!
marusya05 [52]
Answer: D
(0,-4) (12,6)
slope= 10/12
slope== 5/6
y=5/6x+b
-4=0+b
b=-4
the equation of the line is
y=5/6x-4

6 0
3 years ago
Other questions:
  • Can someone please answer this ​
    13·2 answers
  • Tom built a fence around his rectangular shaped pool. The posts are 2 yards apart, there are 4 posts along the width and 8 posts
    7·1 answer
  • Hello please help posted picture of question
    6·1 answer
  • Are there any lines that cannot be written in standard form? If so which ones?
    14·1 answer
  • F(n)=2n+1<br> g(n)=3n<br> Find f(n)+g(n)
    14·1 answer
  • Suppose<br> f(x) = x3 + 3. Find the graph of<br> 2<br> f<br> 3<br> х
    5·2 answers
  • Please help me circles.....
    15·2 answers
  • Rearrange y= -3/4x + 2 in standard form with a positive lead to coefficient
    15·1 answer
  • Divide 24 apples between Roopa and Amita in ratio 5:7
    7·2 answers
  • Practice A<br><br> In Exercises 1-3, find the value of x. Write your answer in simplest form.
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!