The population (in millions) of a certain country t years after 1900 is given by the function p(t). there were 480 million in 1900. if p′(t)=3 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)=3 )

The population of the country in 1907 was 501 million.

Step-by-step explanation:

Hi there!

The population is given by the function p(t)

We know that p(0) = 480 million and that p´(t) = 3.

p´(t) is the derivative of the function p(t) and expresses the variation (or rate of change) of the population with respect to "t". In this case, p´(t) = 3 indicates that the population increases by 3 million per year (because t is in years) from 1900 to 1910. Then, in 1907 the population will be:

480 million + 3 million / year · 7 year = 501 million.

- 2 + 10x³ - 21x² + 19x - 4

step-by-step explanation:

each term in the second factor is multiplied by each term in the first factor

x²(- 2x² + 4x - 1) - 3x(- 2x² + 4x - 1) + 4(- 2x² + 4x - 1) ← distribute

= - 2 + 4x³ - x² + 6x³ - 12x² + 3x -8x² + 16x - 4

collect like terms

= - 2 + 10x³ - 21x² + 19x - 4 ← in standard form

$8

step-by-step explanation:

it is pretty much backwards.

you take the 4x2 multiply that, and that is = $8