Answer: 4
Step-by-step explanation:
Perpendicular lines have reciprocal slopes
Answer:
an exponential growth function to represent this situation is:
![x\left(t\right)=100,000\times \left(1.09\right)^t\:](https://tex.z-dn.net/?f=x%5Cleft%28t%5Cright%29%3D100%2C000%5Ctimes%20%5Cleft%281.09%5Cright%29%5Et%5C%3A)
Step-by-step explanation:
We know that the exponential growth function is of the form
![x\left(t\right)\:=\:x_0\:\times \:\left(1\:+\:r\right)^t](https://tex.z-dn.net/?f=x%5Cleft%28t%5Cright%29%5C%3A%3D%5C%3Ax_0%5C%3A%5Ctimes%20%5C%3A%5Cleft%281%5C%3A%2B%5C%3Ar%5Cright%29%5Et)
where
- x(t) represents the value at time t
- x₀ represents the initial value at time t = 0. In other words, it is the initial value (the amount before measuring growth or decay)
- r represents the growth factor when r > 0 and decay factor when r < 0
- t represents the of time intervals that have passed
In our case,
Given that
A social media website had 100,000 followers its first year. Thus,
The number of followers increased by 9% each year. Thus,
Thus, substituting r = 0.09 and x₀ = 100,000 in the growth function
![x\left(t\right)\:=\:x_0\:\times \:\left(1\:+\:r\right)^t](https://tex.z-dn.net/?f=x%5Cleft%28t%5Cright%29%5C%3A%3D%5C%3Ax_0%5C%3A%5Ctimes%20%5C%3A%5Cleft%281%5C%3A%2B%5C%3Ar%5Cright%29%5Et)
![x\left(t\right)=100,000\times \left(1+0.09\right)^t\:](https://tex.z-dn.net/?f=x%5Cleft%28t%5Cright%29%3D100%2C000%5Ctimes%20%5Cleft%281%2B0.09%5Cright%29%5Et%5C%3A)
![x\left(t\right)=100,000\times \left(1.09\right)^t\:](https://tex.z-dn.net/?f=x%5Cleft%28t%5Cright%29%3D100%2C000%5Ctimes%20%5Cleft%281.09%5Cright%29%5Et%5C%3A)
Therefore, an exponential growth function to represent this situation is:
![x\left(t\right)=100,000\times \left(1.09\right)^t\:](https://tex.z-dn.net/?f=x%5Cleft%28t%5Cright%29%3D100%2C000%5Ctimes%20%5Cleft%281.09%5Cright%29%5Et%5C%3A)
Answer:
Area of the circle with diameter 14cm is 154.35 cm squared.
Step-by-step explanation:
Since d=2r, we know that r=1/2D=7cm
We also know that the area of a circle can be found using the following equation: pir^2
We can plug in pi=3.14 and r=7 to get
area=(3.14)(7)^2=3.14*49=154.35cm^2
Answer:
2.9%
Step-by-step explanation:
The problem says the stations are 260 feet apart. Assuming that this is the horizontal distance between them, then the grade is:
7.5 / 260 × 100% = 2.9%
This is less than the maximum of 3.5%, so it meets the standards.