Question

The gross national product (GNP) of a certain country was N(t)= (t)^2+5t+106 billion dollars, t years after 2000. At what rate was GNP changing with respect to time in 2008?

Answer 1

1)you must DERIVE THE FUNCTION t^2 + 5t +106, it represents the variation , dy/dt = 2t+5

now , substitute it value in the equation

N(8) = 2(8)+5 = 21

Answer 2

In 2008, the GNP was changing at the rate of 21 billions of dollars per year in 2008.

Explanation:

The GNP of a country is given by the following function:

`N(t) = t^(2) + 5t + 106`

In which N(t) is calculated in billions of dollars.

The rate of change of the GNP after t years is:

`N'(t) = 2t + 5`

Calculated in billions of dollars per year.

At what rate was GNP changing with respect to time in 2008?

2008 is 2008-2000 = 8 years after 2000. So this is N'(8).

`N'(t) = 2t + 5`

`N'(8) = 2*8 + 5`

`N'(8) = 21`

In 2008, the GNP was changing at the rate of 21 billions of dollars per year in 2008.