### Home > PC3 > Chapter 6 > Lesson 6.1.3 > Problem6-57

6-57.

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?

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?

$20000=1000e^{0.2t}$

$20=e^{0.2t}$

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