Desmos Graphing Calculator

CalcReferenceCopy

Math·Algebra·Linear functions

hard

A beekeeper’s initial observation of the population of a certain bee colony was $1,600$ bees. The beekeeper set a goal to increase the population to $2,975$ bees. The beekeeper uses a model that predicts the population of this bee colony begins at $1,600$ and increases by $110$ bees per week in the first two weeks after the initial observation, and then increases by $165$ bees per week until the beekeeper’s goal is reached. According to this model, at the end of week $w$ after the initial observation, where $w>2$, which of the following functions gives the predicted number of bees still needed to reach the beekeeper’s goal?

A

$p(w)=-110+165w$

B

$p(w)=1,485-165w$

C

$p(w)=2,865+165w$

D

$p(w)=2,975-165w$