Answer: No real solution
Step-by-step explanation:
A] amplitude = 3 feet; period = 16 hours; midline: y = 5
Hope this helps (:
The answer would be irrational
There are many solutions to 24
0 + 24 = 24
6 x 4 = 24
192/8 = 24
![(-1, 9), \ (0, 6), \ (1, 4), \ (2, 2\frac{2}{3} ), \ (1, \frac{7}{9} )](https://tex.z-dn.net/?f=%28-1%2C%209%29%2C%20%5C%20%280%2C%206%29%2C%20%5C%20%281%2C%204%29%2C%20%5C%20%282%2C%202%5Cfrac%7B2%7D%7B3%7D%20%29%2C%20%5C%20%281%2C%20%5Cfrac%7B7%7D%7B9%7D%20%29)
Solution:
Given ![f(x)=6\left(\frac{2}{3}\right)^{x}](https://tex.z-dn.net/?f=f%28x%29%3D6%5Cleft%28%5Cfrac%7B2%7D%7B3%7D%5Cright%29%5E%7Bx%7D)
Domain = {–1, 0, 1, 2, 3}
Substitute the given values in the function.
At x = –1,
![f(-1)=6\left(\frac{2}{3}\right)^{-1}](https://tex.z-dn.net/?f=f%28-1%29%3D6%5Cleft%28%5Cfrac%7B2%7D%7B3%7D%5Cright%29%5E%7B-1%7D)
![=6 \times \frac{3}{2}](https://tex.z-dn.net/?f=%3D6%20%5Ctimes%20%5Cfrac%7B3%7D%7B2%7D)
= 9
![(x, f(x))=(-1, 9)](https://tex.z-dn.net/?f=%28x%2C%20f%28x%29%29%3D%28-1%2C%209%29)
At x = –0,
![f(0)=6\left(\frac{2}{3}\right)^{0}=6](https://tex.z-dn.net/?f=f%280%29%3D6%5Cleft%28%5Cfrac%7B2%7D%7B3%7D%5Cright%29%5E%7B0%7D%3D6)
![(x, f(x))=(0,6)](https://tex.z-dn.net/?f=%28x%2C%20f%28x%29%29%3D%280%2C6%29)
At x = 1,
![f(1)=6\left(\frac{2}{3}\right)^{1}=4](https://tex.z-dn.net/?f=f%281%29%3D6%5Cleft%28%5Cfrac%7B2%7D%7B3%7D%5Cright%29%5E%7B1%7D%3D4)
![(x, f(x))=(1,4)](https://tex.z-dn.net/?f=%28x%2C%20f%28x%29%29%3D%281%2C4%29)
At x = 2,
![f(2)=6\left(\frac{2}{3}\right)^{2}](https://tex.z-dn.net/?f=f%282%29%3D6%5Cleft%28%5Cfrac%7B2%7D%7B3%7D%5Cright%29%5E%7B2%7D)
![=\frac{24}{9}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B24%7D%7B9%7D)
(Cancel the common terms)
![(x, f(x))=(2, 2\frac{2}{3} )](https://tex.z-dn.net/?f=%28x%2C%20f%28x%29%29%3D%282%2C%202%5Cfrac%7B2%7D%7B3%7D%20%29)
At x = 3,
![f(3)=6\left(\frac{2}{3}\right)^{3}](https://tex.z-dn.net/?f=f%283%29%3D6%5Cleft%28%5Cfrac%7B2%7D%7B3%7D%5Cright%29%5E%7B3%7D)
(Cancel the common terms)
![=\frac{16}{9}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B16%7D%7B9%7D)
![(x, f(x))=(3, 1\frac{7}{9} )](https://tex.z-dn.net/?f=%28x%2C%20f%28x%29%29%3D%283%2C%201%5Cfrac%7B7%7D%7B9%7D%20%29)
Plot the points in the graph.
The image of the graph is attached below.