When records were first kept (t=0), the population of a rural town was 260 people. During the following years, the population grew at a rate of P'(t) = 45(1+sqrt(t)).

a) what is the population after 15 years?
b) find the popuation P(t) at any time t > 0.

(a) The population after 15 years is 2678.

(b)Therefore the population P(t) at any time t>0 is

Step-by-step explanation:

Given that,

The population grew at a rate of

Integrating both sides

             [ c is integration constant]

When t=0 , P(0)= 260

Therefore the population P(t) at any time t>0 is

To find the population after 15 years, we need to plug t=15 in the above expression.

         ≈2678

The population after 15 years is 2678.

both graphs increase on their domain

neither graph has a y-intercept

step-by-step explanation:

the following points can be visualized easily from the graph