Suppose a program takes $400$ milliseconds to process input of size $50.$ If the runtime ${?}^{+}$is T$($n$)=$ kn$4,$ where n is the input size, how long will the program take to process input of size $...($see below$)$

a$)100?\_\_\_\_\_\_\_\_\_\_\_\_\_$

b$)500?\_\_\_\_\_\_\_\_\_\_\_\_\_$

c$)25?\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

Justify your answers using an applicable rules of thumb.