Depends on which rate of change you're talking about. The rate of change is another term for a slope of a function. There's two(2) different version of rate of change.
First version one is the instantaneous rate of change. aka derivative. This one is found simply by taking the derivative of a function.
Second version is the average rate of change, which is found using the slope formula, (y₂ - y₁)/(x₂ - x₁)
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Initial value problem should give you an initial point (x, y) to plug into your function. You plug those x,y value in to find your answer.
There's variation of initial value problems so I can't give you any specific details on how to do it unless you can post the question.
52s + 30b because 52 x s + 30 x b = 52s + 30b
If your solving for x, you need to isolate/get the variable "x" by itself in the inequality:
-24 ≤ 3x - 9 First add 9 on both sides
-24 + 9 ≤ 3x - 9 + 9
-15 ≤ 3x Then divide 3 on both sides to get "x" by itself

-5 ≤ x [or x ≥ -5 if you prefer "x" to be on the left side]
Both solutions:
x = -1, -7/3
> y(1) = -5x + 3
-3. -3
> -2 = -5x
÷-5. ÷-5
= 0.4 = x