# Can someone help me with this ques?

• Oct 11th 2009, 03:43 PM
mathcalculushelp
Can someone help me with this ques?
A certain country's Gross Domestic product (in millions of dollars) t years since the beginning of 1997 is given by

G(t)= -2.4t^3 + 48t^2 + 18t + 8000
for o<t<12 . Determine the year that GDP is growing at a rate of at least \$275 000 000 per year.Also,determine whether or not the growth rate of GDP drops back below that rate of growth, if so,the year that it happens.
• Oct 11th 2009, 03:47 PM
Epiphenomenon
Quote:

Originally Posted by mathcalculushelp
A certain country's Gross Domestic product (in millions of dollars) t years since the beginning of 1997 is given by

G(t)= -2.4t^3 + 48t^2 + 18t + 8000
for o<t<12 . Determine the year that GDP is growing at a rate of at least \$275 000 000 per year.Also,determine whether or not the growth rate of GDP drops back below that rate of growth, if so,the year that it happens.

Take the first derivative with respect to time, and then set that equal to \$275 million. Then, solve for t. Add t to 1997 (round up), and this will give you the year it will be growing at a rate of at least \$275 M.
• Oct 11th 2009, 04:07 PM
mathcalculushelp
thanks!
• Oct 11th 2009, 06:15 PM
mathcalculushelp
Finding t ..?
If I take the 1st derivative of the function then it is

-7.2t^2+96t+18..

Iam setting this equal to 275000000 but unable to find t from it.Can somebody help me pls?
• Oct 11th 2009, 06:21 PM
mr fantastic
Quote:

Originally Posted by mathcalculushelp
If I take the 1st derivative of the function then it is

-7.2t^2+96t+18..

Iam setting this equal to 275000000 but unable to find t from it.Can somebody help me pls?

You're meant to solve 275 = -7.2t^2+96t+18 since the unit is millions of dollars per year. Now re-arrange this equation into the form of