A colony of grasshoppers have infested a farmer’s land. The farmer investigated the area one week ago and found that in one acre there were approximately $1000$ grasshoppers. He also determines that the population of the insects can be modeled by the function $P\left(t\right) = 1000e^{0.2t}$, where $t$ is the time in days from his initial inspection.  

1. Assuming the grasshoppers continue to increase according to the farmer’s model, what is the population now?

   Hint (a):

   Since the initial inspection was one week ago, evaluate $P\left(7\right)$.

2. The crops will be destroyed if the population reaches $20,000$ per acre. How long does the farmer have before this occurs?

   Step 1(b):

   $20000=1000e^{0.2t}$

   Step 2(b):

   $20=e^{0.2t}$

   Step 3(b):

   $\ln\left(20\right)=lm\left(e^{0.2t}\right)$