PHYSICS HOMEWORK HELP-CAN SOMEONE PLEASE EXPLAIN

Question

Function y(t)=e^-t/T. Here T is the time constant and has units of s^-1. If the time constant T=4 s, what is the approximate value of the function at time t=4s?

Answer 1

Hello. Lets see if I can help you.

The function y(t) = e^-t/T

We want to evaluate the function at t = 4.

y(4) = e^-4/T

We are also told that T (the time constant) is equal to 4 s^-1. So T = 4.

we can now rewrite the function evaluated at t = 4 as,

y(4) = e^-4/4 = e^-1 = 1/e

the symbol 'e' is known as Euler's number and is equal to 2.71828 when we round it off to 5 decimal places. This is a similar idea to the number Pi or π.

So y(4) = 1/e ≈ 1/2.71828 ≈ 0.367879

Hope this helps!