Constant is the scale term in proportionality. Suppose one variable is dependent on the other and one variable become twice, other becomes also twice and if one becomes half, other too becomes half., but they are two different variables which are no-where linked (like cost(money) vs quantity). Quantity and cost are two different things but they abridge a mathematical relation of proportionality. So in the mathematics to abridge these two different variables, we need something. Constant serves that purpose.
By letting

we get derivatives


a) Substitute these into the differential equation. After a lot of simplification, the equation reduces to

Examine the lowest degree term
, which gives rise to the indicial equation,

with roots at r = 0 and r = 4/5.
b) The recurrence for the coefficients
is

so that with r = 4/5, the coefficients are governed by

c) Starting with
, we find


so that the first three terms of the solution are

55+10.00x ≥ 150 x ≥ 9.5 hours I hope that helps
Answer:
The function rule is

Step-by-step explanation:
The given ordered pairs are (0,-1), (1,0),(2,3),(3,8),(4,15)
We can observe the following pattern.





When we generalize this pattern, we obtain:

This is the function equation.
The function rule is
