Biologists Estimate That the Population of a Biological Colony at Time

Multiple Choice

Biologists estimate that the population of a biological colony at time t (in minutes) is $P ( t ) = P _ { 0 } e ^ { k t }$ thousand, where $P _ { 0 }$ and k are positive constants. If the population is 1,000 after 20 minutes and is known to double every hour, what is the population after 40 minutes? Round to the nearest whole number.

A) 1,258
B) 1,259
C) 1,260
D) 1,261