The expression log₂(10) tells us when the population reaches 10,000 and the equation 7 = log₂(128) tells us that the population reaches 128,000 in 7 days.
<h3>What is an
exponential function?</h3>
An exponential function is in the form:
y = abˣ
Where a is the initial value of y and b is the multiplication factor.
Let p represent the bacteria population in thousand after d days.
Since each day, the bacteria population grows by a factor of 2, hence:
![p=2^d](https://tex.z-dn.net/?f=p%3D2%5Ed)
Hence, d = log₂p represents a logarithmic function
The expression log₂(10) tells us when the population reaches 10,000 and the equation 7 = log₂(128) tells us that the population reaches 128,000 in 7 days.
Find out more on exponential function at: brainly.com/question/12940982
Answer: Here are two inequalities. Hope this is good.
4<x<9
9>x<4
The median is the number in the middle of a list of numbers.
Since this list has an even amount of numbers, you take the 2 middle numbers, add it together, and divide by 2 to get the average value.
The middle values are 17 and 20, so you do:
17 + 20 = 37 now divide by 2
37/2 = 18.5
Answer:
![(\sqrt{2})^3](https://tex.z-dn.net/?f=%28%5Csqrt%7B2%7D%29%5E3)
Step-by-step explanation:
Given the expression
![(x - \frac{1}{x} )^3](https://tex.z-dn.net/?f=%28x%20-%20%5Cfrac%7B1%7D%7Bx%7D%20%29%5E3)
Simplify
![(\frac{x^2-x}{x} )^3](https://tex.z-dn.net/?f=%28%5Cfrac%7Bx%5E2-x%7D%7Bx%7D%20%29%5E3)
Given that x = 1+√2
Substitute
![(\frac{(1+\sqrt{2} )^2-(1+\sqrt{2} )}{1+\sqrt{2} } )^3\\=( \frac{1+2\sqrt{2} +2 - 1 - \sqrt{2}}{1+\sqrt{2}} )^3\\= (\frac{\sqrt{2}+2}{1+\sqrt{2}})^3 \\Rationalize\\= (\frac{\sqrt{2}-2+2-2\sqrt{2}}{1-2})^3 \\=( \frac{-\sqrt{2}}{-1})^3 \\= (\sqrt{2})^3\\ \\](https://tex.z-dn.net/?f=%28%5Cfrac%7B%281%2B%5Csqrt%7B2%7D%20%29%5E2-%281%2B%5Csqrt%7B2%7D%20%29%7D%7B1%2B%5Csqrt%7B2%7D%20%7D%20%29%5E3%5C%5C%3D%28%20%5Cfrac%7B1%2B2%5Csqrt%7B2%7D%20%2B2%20-%201%20-%20%5Csqrt%7B2%7D%7D%7B1%2B%5Csqrt%7B2%7D%7D%20%29%5E3%5C%5C%3D%20%28%5Cfrac%7B%5Csqrt%7B2%7D%2B2%7D%7B1%2B%5Csqrt%7B2%7D%7D%29%5E3%20%5C%5CRationalize%5C%5C%3D%20%28%5Cfrac%7B%5Csqrt%7B2%7D-2%2B2-2%5Csqrt%7B2%7D%7D%7B1-2%7D%29%5E3%20%5C%5C%3D%28%20%5Cfrac%7B-%5Csqrt%7B2%7D%7D%7B-1%7D%29%5E3%20%5C%5C%3D%20%28%5Csqrt%7B2%7D%29%5E3%5C%5C%20%5C%5C)