Answer:
[tex]a(n)=46-(n-1) \times 4[/tex]
Step-by-step explanation:
It's important to know that the graph is showing a linear function, which means its equation cannot be exponential. So, choices A and B are not correct here.
To find the correct equation, we could find the slope first with the following formula and the two given points
[tex]m=\frac{y_{2}-y_{1} }{x_{2} -x_{1} }\\ m=\frac{26-30}{6-5}=4[/tex]
Now, we use the point-slope formula to find the equation
[tex]y-y_{1} =m(x-x_{1} )\\y-30=4(x-5)\\y=4x-20+30\\y=4x+10[/tex]
Notice that choice C has the same coefficient of 4, which is the slope of the line. Therefore, that's the right answer.
Let's prove it for [tex]n=6[/tex]
[tex]a(n)=46-(n-1) \times 4\\a(6)=46-(6-1) \times 4=46-20=26[/tex]
As the table shows.
Therefore, choice C is correct.
