Question

The population (in millions) of a certain country t years after 1900 is given by the function p(t). There were 420 million in 1900. If p′(t)=7 throughout the time span 1900 to 1910, what was the population of the country in 1907? (Hint: What was the practical signifigance of p′(t)=7 )?

Answer 1

Answer:469 million

Step-by-step explanation:

Given

The population of a country at t=1900 is 420 million

and P'(t) is a constant therefore P(t) is a linear function of time

assuming P(t)=7t +c

at t=0 i.e. 1900 at starting Point P(t)=420 million

i.e.

$420=7\times 0+c$

$c=420 million$

Thus $at\ t=7\ year\ later\ i.e.\ 1907$

$P(t)=7\times 7+420=469 million$

Thus at 1907 Population is 469 million

P'(t)=7 indicates that growth rate of Population is constant equals to 7 billion