Desmos Graphing Calculator

CalcReferenceCopy

Math·Advanced Math·Nonlinear functions

medium

Nina is selling coins from her coin collection. When she started selling the coins, there were $2,600$ coins in the collection. At the end of each week for $3$ weeks after Nina started selling the coins, the number of coins in the collection had decreased by $\frac{1}{2}$ of the coins in the collection at the end of the previous week. Which equation gives the number of coins, $c$, in the collection $w$ weeks after Nina started selling the coins, where $0\le w\le 3$?

A

$c=w^{\frac{1}{2}}$

B

$c=2,600^w$

C

$c=1,300{\left(\frac{1}{2}\right)}^w$

D

$c=2,600{\left(\frac{1}{2}\right)}^w$