Answer:
Part 1) [tex]d(x)=5(\frac{1}{3})^{x}[/tex] ----> The y-intercept is the point (0,5), graph initially decreases rapidly and then decreases slowly
Part 2) [tex]g(x)=(\frac{2}{5})^{x}[/tex] ----> The y-intercept is the point (0,1), graph initially decreases rapidly and then decreases slowly
Part 3) [tex]h(x)=(4)^{x}[/tex] ----> The y-intercept is the point (0,1),graph initially increases slowly and then increases rapidly
Step-by-step explanation:
Part 1) we have
[tex]d(x)=5(\frac{1}{3})^{x}[/tex]
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
[tex]d(0)=5(\frac{1}{3})^{0}=5[/tex]
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
[tex]g(x)=(\frac{2}{5})^{x}[/tex]
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
[tex]g(0)=(\frac{2}{5})^{0}=1[/tex]
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
[tex]h(x)=(4)^{x}[/tex]
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
[tex]h(0)=(4)^{0}=1[/tex]
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
