Mathematics

Problem

A radar signal pulse is modeled by the function

P(t)

on the time interval

[0, 50]\,\mu\text{s}

. An engineer needs to compress this signal to fit exactly into a

10\,\mu\text{s}

slot starting at

t = 100\,\mu\text{s}

. If the transformed signal is

P(at + b)

, find the values of

a

and

b