All categories

3 years ago

Half of the substance to remain is called the half-life of the substance.

Mathematics

1 answer:

Sindrei [870]3 years ago

5 0

Answer:

Instructions are below.

Step-by-step explanation:

<u>To calculate the final amount if a given substance, we need to use the following formula:</u>

final amount= initial amount / (2^n)

n= elapsed time / half-life

For 20 years:

n= 20/10= 2

Final amount= 200/(2^2)

Final amount= 50 grams

For 60 years:

n= 60/10= 6

Final amount= 200/ (2^6)

Final amount= 3.125 grams

<u>To calculate the elapsed time it is more complicated:</u>

elapsed time= ln(ending amount/beginning amount) / (-decay constant)

ln= natural logarithm

decay constant= ln(2) / half-life

decay constant= 0.0693

elapsed time= ln(1.03/200) / (-0.0693)

elapsed time= 76.028

Prove:

n= 76.02/10= 7.602

Final amount= 200/(2^7.602)= 1.03 grams

You might be interested in

Determine whether each table represents a linear quadratic or exponential function

Kryger [21]

Answer:

Table A: exponencial function

Table B: quadratic function

Table C: linear function

Step-by-step explanation:

Table A:

for x from 1 to 2, Y increased by 6

for x from 2 to 3, Y increased by 18

for x from 3 to 4, Y increased by 54

So we can see that the values of Y are being multiplied by 3 for each increment of x, so this table represents an exponencial function.

Table B:

for x from 1 to 2, Y increased by 6

for x from 2 to 3, Y increased by 10

for x from 3 to 4, Y increased by 14

The increment of Y is higher than a linear increment and smaller than an exponencial increment, so this is the quadratic function.

Table C:

for x from 3 to 6, Y increased by -2

for x from 6 to 9, Y increased by -2

for x from 9 to 12, Y increased by -2

The increment of Y is constant for the same increment of X, so this is a linear function.

7 0

3 years ago

Is there a transformation that maps shape 1 onto shape 4?

Llana [10]

Answer:

1 place to the left and 2 places down

Step-by-step explanation:

(+1,-2)

5 0

3 years ago

Omar has 2 3/4 cups of dough to make dumplings. If he use 3/16 cup of dough for each dumpling, how many whole dumplings can Omar

andrey2020 [161]

Answer:

Step-by-step explanation:

Omar can make 14 whole dumplings. You change 2 3/4 cups to an improper fraction ( multiply the denominator and add the numerator ) and you get 11/4. Since you need 3/16 cups for one dumpling you have to find the greatest common denominator which is 16. You multiply 4 by 11 to get the numerator and end up with 44/16. Since you need 3/16 for one whole dumping you divide 44 by 3 and get 14.6 repeating. You cannot have a fraction of a dumpling so you round down and get the answer 14.

5 0

3 years ago

Use the picture below to solve for the missing information, given PQ = 2x + 8, QR = x + 11, and PR = 5x - 3.

Ann [662]

Answer:

Step-by-step explanation:

I think x=-2

6 0

2 years ago

Classify each function as even, odd, or neither even nor odd.

drek231 [11]

The function

f(x) is even

g(x) is neither even nor odd

h(x) is odd

Steps:

for an even function it holds that f(-x) = f(x):

f(-x) = (-1)^6 x^6 - (-1)^4 x^ 4 = x^6 - x^4 = f(x) => f is even

for an odd h(x) it holds that h(-x) = -h(x):

$h(-x) = (-1)^5x^5-(-1)^3x^3 = -(x^5-x^3) = -h(x) \implies h(x)\,\, \mbox{even}$

It is easy to show that g(x) does not match any of the two possibilities above.

8 0

3 years ago

Read 2 more answers