Answer:
Step-by-step explanation:
From the information given,
Let the two digits that Chen writes down to be p and q
where,
q will be in the unit place and p will be in the tens place.
So, the value of the digit = 10p + q
So, if he swapped the number, he will have 10q + p
However,
the new number determined is thrice more than the 1/3 pf the original number.
i.e
the 1/3rd of the original number = 
=
thrice more than that will be = 
∴
multiply through by 3, we have :
10p+q + 9 = 30q + 3p
collecting the like terms, we have:
10p - 3p +q -30q +9 = 0
7p - 29q +9 = 0
7p - 29q = -9
Therefore, p,q lie between 0 and 9
Therefore, the possibility of the original number is p = 7 and q = 2
Step Number 1. is to Simplify
Step Number 2. <span>Simplify so you get </span>
Done! :)
Power rule of exponents says that the power of the power of a exponent is equal to the multiplying both the powers. The expression which is equal to the given expression is,
The option B is the correct option.
Given information-
The given expression in the problem is,
![[(r)^{-7}]^5](https://tex.z-dn.net/?f=%5B%28r%29%5E%7B-7%7D%5D%5E5)
<h3>Power rule of exponents</h3>
Power rule of exponents says that the power of the power of a exponent is equal to the multiplying both the powers.
Suppose<em> </em><em>x</em> is a number with power <em>a. </em>The power is power of the power of number <em>x. </em>Then by the power rule of the exponents,
Using the power rule of the exponents given expression can be written as,
![[(r)^{-7}]^6=(r)^{-7\times 6} ](https://tex.z-dn.net/?f=%5B%28r%29%5E%7B-7%7D%5D%5E6%3D%28r%29%5E%7B-7%5Ctimes%206%7D%20%0A)
![[(r)^{-7}]^6=(r)^{-42}](https://tex.z-dn.net/?f=%5B%28r%29%5E%7B-7%7D%5D%5E6%3D%28r%29%5E%7B-42%7D)
<h3>Negative exponents rule</h3>
Negative exponents rule says that when a power of a number is negative, then write the number in the denominator with the same power with positive sign.Thus,
![[(r)^{-7}]^6=\dfrac{1}{(r)^{42}}](https://tex.z-dn.net/?f=%5B%28r%29%5E%7B-7%7D%5D%5E6%3D%5Cdfrac%7B1%7D%7B%28r%29%5E%7B42%7D%7D%20)
Hence the expression which is equal to the given expression is,
The option B is the correct option.
Learn more about the power rule of exponents here;
brainly.com/question/819893
Step-by-step explanation:
(a) dP/dt = kP (1 − P/L)
L is the carrying capacity (20 billion = 20,000 million).
Since P₀ is small compared to L, we can approximate the initial rate as:
(dP/dt)₀ ≈ kP₀
Using the maximum birth rate and death rate, the initial growth rate is 40 mil/year − 20 mil/year = 20 mil/year.
20 = k (6,100)
k = 1/305
dP/dt = 1/305 P (1 − (P/20,000))
(b) P(t) = 20,000 / (1 + Ce^(-t/305))
6,100 = 20,000 / (1 + C)
C = 2.279
P(t) = 20,000 / (1 + 2.279e^(-t/305))
P(10) = 20,000 / (1 + 2.279e^(-10/305))
P(10) = 6240 million
P(10) = 6.24 billion
This is less than the actual population of 6.9 billion.
(c) P(100) = 20,000 / (1 + 2.279e^(-100/305))
P(100) = 7570 million = 7.57 billion
P(600) = 20,000 / (1 + 2.279e^(-600/305))
P(600) = 15170 million = 15.17 billion
