Question

Irene reads that the 2004 census of whooping cranes tallied 213 birds which is 19 greater than 2003 the growth can be modeled using P(t) = P(0) e^kt what is k

Answer 1

Answer: The value of k is 0.09.

Step-by-step explanation:

Since we have given that

$P(t)=P(0)e^{kt}$

Here, k is the rate ,

t is the time,

In 2004, the whooping cranes tallied 213 birds,

So, P(t)=213

It is 19 greater than 2003,

So, P(0)=213-19=194

So, substitute all the values in given expression:

$213=194e^{k.1}\\\\\dfrac{213}{194}=e^k\\\\1.098=e^k\\\\\text{Taking log on both the side}\\\\\ln 1.098=k\\\\k=0.09$

Hence, the value of k is 0.09.