<em>There is no specific requirement in the question, but I'm assuming you need to compute the time needed for Alexis reach 1,000,000 Instagram followers</em>
Answer:
![t= 462.82\ days](https://tex.z-dn.net/?f=t%3D%20462.82%5C%20days)
Step-by-step explanation:
<u>Exponential Growth
</u>
When the number of observed elements grows as the previous value multiplied by a constant ratio, we have exponential growth. The formula to model such situations is
![\displaystyle f(x) = f_o(1 + r)^t](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%28x%29%20%3D%20f_o%281%20%2B%20r%29%5Et)
Where
is the initial value of f, 1 + r is the constant ratio, and t is the time expressed in half days (12 hours)
The initial value is 100 Instant followers, thus:
![\displaystyle f(x) = 100(1.01)^t](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%28x%29%20%3D%20100%281.01%29%5Et)
We need to know when the number of followers will reach 1,000,000. Setting up the equation
![\displaystyle 100(1.01)^t=1,000,000](https://tex.z-dn.net/?f=%5Cdisplaystyle%20100%281.01%29%5Et%3D1%2C000%2C000)
Simplifying by 100
![\displaystyle (1.01)^t=10,000](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%281.01%29%5Et%3D10%2C000)
Taking logarithms
![\displaystyle t\ log(1.01)=log\ 10,000](https://tex.z-dn.net/?f=%5Cdisplaystyle%20t%5C%20log%281.01%29%3Dlog%5C%2010%2C000)
![\displaystyle t\ log(1.01)=4](https://tex.z-dn.net/?f=%5Cdisplaystyle%20t%5C%20log%281.01%29%3D4)
Solving for t
periods of 12 hrs
![t= 462.82\ days](https://tex.z-dn.net/?f=t%3D%20462.82%5C%20days)
Answer:
28
Step-by-step explanation:
4x + 9x + 8x = 147
21x = 147
x = 147/21
x = 7
========
The shortest side will be 4x
4*7 = 28
Using the quadratic equation we get:
![\frac{ - 2 + - \sqrt{4 - 32} }{2} = \frac{ - 2 + - \sqrt{ - 28} }{2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20-%202%20%2B%20-%20%5Csqrt%7B4%20-%2032%7D%20%7D%7B2%7D%20%3D%20%5Cfrac%7B%20-%202%20%2B%20-%20%5Csqrt%7B%20-%2028%7D%20%7D%7B2%7D%20)
Factoring out 2 we get
![\frac{ - 2 + - 2\sqrt{ - 7} }{2} = - 1( + - ) \sqrt{ - 7}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20-%202%20%2B%20-%202%5Csqrt%7B%20-%207%7D%20%7D%7B2%7D%20%3D%20-%201%28%20%2B%20-%20%29%20%5Csqrt%7B%20-%207%7D%20)
Factoring out the imaginary number:
![- 1 + \sqrt{7} i \: (and) \: - 1 - \sqrt{7} i](https://tex.z-dn.net/?f=%20-%201%20%2B%20%5Csqrt%7B7%7D%20i%20%5C%3A%20%28and%29%20%5C%3A%20-%201%20-%20%5Csqrt%7B7%7D%20i)
So b.
3/4= j-1/2
first to add 1/2 to both sides to solve for j
3/4 + 1/2= j
second you find a common denominator in order to add 3/4 and 1/2, the common denominator would be 4, you would have to change 3/4 at all because the denominator is already 4 but in order to make the denominator of 1/2, 4 you would have to multiply both the denominator and numerator by 2 so
3/4 + 2/4 = 5/4
so 5/4 =j
to check your answer you plug 5/4 in for j
3/4 = 5/4 -1/2
again you need to find a common denominator between 5/4 and 1/2 which again would be 4, and again you wouldn't change 5/4 but you would multiply both the numerator and the denominator of 1/2 so
3/4= 5/4-2/4
5-2= 3 and you would keep the 4 so
5/4 - 2/4 = 3/4
so j = 5/4
Answer:
6x + 4 = -8
Step-by-step explanation:
6 (-2) = -12
-12 + 4 = -8
Hope this helps!