Question

A quantity increases according to the exponential function y(t)=y0ekt. a. What is the tripling time? b. What is the time required for the quantity to increase p-fold?

Answer 1

Explanation:

Given

A quantity is increasing according to

`y(t)=y_0e^(kt)`

time taken to triple the initial Quantity

i.e.
`y(t)=3 y_0`

`3y_0=y_0e^(kt)`

`3=e^(kt)`

Taking log on both side

`\ln 3=kt`

`t=(\ln 3)/(k)`

(b)Time required to increase P-fold

i.e.
`y(t)=Py_0`

`Py_0=y_0e^(kt)`

`P=e^(kt)`

taking log both sides

`t=(\ln P)/(k)`