Answer:
Ok, an exponential decay is written as:
P(t) = A*(1 - r)^t
Where A is the initial population, r is the rate of decay and t is the unit of time.
We know that the initial population is 15g
then:
P(t) = 15g*(1 - r)^t
And at t = 3hs, the populations is 5g
P(5h) = 5g = 15g*(1 - r)^5
5/15 = 1/3 = (1 - r)^5
(1/3)^(1/5) = (1 - r) = 0.8
Now, the half life time of the sustance is t = x, such that the population reduces to it's half:
P(x) = A/2 = 15g/2 = 7.5g
Then:
7.5g = 15g*0.8^x
7.5g/15g = 1/2 = 0.8^x
Now, remember that if we have:
a = b^x
then
x = ln(a)/ln(b)
ln(1/2)/ln(0.8) = x = 3,11 hours
<span>x^2 - 6x = 7
(x - 7)(x + 1)= 0
x = 7, - 1
The answer is: x = 7, -1.</span>
A.
In the first generation we have 2 ancestors.
In the second generation we have 4 ancestors or

ancestors.
In the third generation we have 8 ancestors ot

ancestors.
We can see that each succesive generation has two times more members. The sum is:

To calculate number of ancestors we can use formula <span>for the sum of a geometric sequence. Geometric sequence is sequence of numbers that differ by a certain factor. This factor is called ratio. Formula is:
</span>

<span>Where:
S -> sum
a1 -> first member of a sequence
r -> ratio
n -> number of elements
For this question:
a1 = 2
r = 2
n = 40
</span>

<span>
b.
1 generation = 25 years
40 generations = 40 * 25 = 1000 years
c.
Total number of people who have ever lived = </span>

Number of ancestors in 40 generations =

The number of ancestors is greater than total number of people who have ever lived. This means that not all ancestors were distinct and that in each generation both men and women had children with more than one partner.
Answer:
B. Doubled
Step-by-step explanation:
The formula to find the circumference of the circle is

Now our problem says that the radius is doubled. Hence the new radius is 2r
Hence the new circumference will be



Hence our circumference gets doubled.
No because 3 to the 2nd power is 9 and 9 to the second power is 81 which both of them added up is 90 and can’t be square rooted to 10. Therefore no