Answer:
Part 1)
----> The y-intercept is the point (0,5), graph initially decreases rapidly and then decreases slowly
Part 2)
----> The y-intercept is the point (0,1), graph initially decreases rapidly and then decreases slowly
Part 3)
----> The y-intercept is the point (0,1),graph initially increases slowly and then increases rapidly
Step-by-step explanation:
Part 1) we have
![d(x)=5(\frac{1}{3})^{x}](https://tex.z-dn.net/?f=d%28x%29%3D5%28%5Cfrac%7B1%7D%7B3%7D%29%5E%7Bx%7D)
Find the y-intercept
Remember that the y-intercept is the value of y when the value of x is equal to zero (initial value)
For x=0
Substitute
![d(0)=5(\frac{1}{3})^{0}=5](https://tex.z-dn.net/?f=d%280%29%3D5%28%5Cfrac%7B1%7D%7B3%7D%29%5E%7B0%7D%3D5)
The y-intercept is the point (0,5)
using a graphing tool
see the attached figure N 1
The graph initially decreases rapidly and then decreases slowly
Part 2) we have
![g(x)=(\frac{2}{5})^{x}](https://tex.z-dn.net/?f=g%28x%29%3D%28%5Cfrac%7B2%7D%7B5%7D%29%5E%7Bx%7D)
Find the y-intercept
Remember that the y-intercept is the value of y when the value of x is equal to zero (initial value)
For x=0
Substitute
![g(0)=(\frac{2}{5})^{0}=1](https://tex.z-dn.net/?f=g%280%29%3D%28%5Cfrac%7B2%7D%7B5%7D%29%5E%7B0%7D%3D1)
The y-intercept is the point (0,1)
using a graphing tool
see the attached figure N 2
The graph initially decreases rapidly and then decreases slowly
Part 3) we have
![h(x)=(4)^{x}](https://tex.z-dn.net/?f=h%28x%29%3D%284%29%5E%7Bx%7D)
Find the y-intercept
Remember that the y-intercept is the value of y when the value of x is equal to zero (initial value)
For x=0
Substitute
![h(0)=(4)^{0}=1](https://tex.z-dn.net/?f=h%280%29%3D%284%29%5E%7B0%7D%3D1)
The y-intercept is the point (0,1)
using a graphing tool
see the attached figure N 3
The graph initially increases slowly and then increases rapidly