An economist estimates that the gross national product (GNP) of a certain country is $G = G _ { 0 } e ^ { k t }$ , where $G _ { 0 }$ and k are positive constants. If the GNP is 110 billion in 1992 and 190 billion in 1994, when will it be 300 billion? Round your answer to whole years.
A) Approximately 5 years from 1992
B) Approximately 27 years from 1992
C) Approximately 4 years from 1992
D) Approximately -1 years from 1992

Question

Quizplus · Accepted Answer

Given the GNP formula $G = G_0 e^{kt}$, we can use the provided GNP values for 1992 and 1994 to find $k$. For 1992 ($t=0$), $G_0 = 110$ billion. For 1994 ($t=2$), $G = 190$ billion. Substituting these into the formula gives $190 = 110e^{2k}$, solving for $k$ gives $k \approx 0.304$. To find when $G = 300$ billion, substitute $G = 300$ and solve for $t$, which gives $t \approx 4$ years from 1992.

An Economist Estimates That the Gross National Product (GNP) of a Certain