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

Answer:

Step-by-step 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

$\ln 3=kt$

$t=\frac{\ln 3}{k}$

(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

$t=\frac{\ln P}{k}$