mathematical modelling recurrence relations equations

Convert this statement into a mathematical equation that describes the recurrence relation. Use α as the constant of proportionality and β as the added constant. Generate an vector with the variable name y, that contains the values of y determined by solving the recurrence relation. You are given the following:

1. 
2. 
3. 
4. 

Plot your solution and observe its behaviour. Assign the numerical value of the correct option to the variable z.

1. The solution diverges to negative infinity.
2. The solution diverges to infinity.
3. The solution decays to zero.
4. The solution decays to a constant.
5. The solution oscillates but converges to a value.
6. The solution oscillates and does not converge.
7. The solution oscillates while diverging to ± infinity.
8. The solution increases to a constant value.