Thread: 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.

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.

thanks!

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?

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

quadratic = 0

and use the quadratic formula to solve for t. Test which of the two solutions is required.