Stuck on homework problem

When t  = 0     we have this equation

n  +  a  =  2       (1)

When t  = 1   we have this equation 

n + m   =   3       (2)

When  t  = 2   we have this equation

n + 2m  - ab^2   = 20      (3)

When  t = 3  we have this equation

n + 3m  =  1     (4)

And  when  t  =4  we have this

n + 4m +  ab^t  =   -162     (5)

Using (2)  and (4) we have that

n + m  = 3

n  + 3m  =  1        subtract the first equation from the second and we have that

2m  =  -2

m  = -1

So....  n =  4

And using (1)

4  +  a  = 2

a  = -2

And using (3)  we have that

n+ 2m  -ab^2  = 20

Subbing we have that

4  + 2(-1)  - (-2)b^2  = 20

2  + 2b^2  = 20

1  + b^2  =  10

b^2  = 9

b =   3  or  b  = -3

Assuming that  b  is positive

So  using 5...if   n = 4, m= -1, a =-2  and  b  = 3    and  t  = 4  we have that

4 - 4  + (-2)(3)^4   =

-2 * 81  = 162

So  

n = 4

m = -1

a = -2

b = 3

Here's a graph using  x  instead of  t  : https://www.desmos.com/calculator/b677bwjlwf