Chapter 16.2, Problem 61E

To determine

To calculate: The rate at which cost in dollars per week is increasing on January $1,2011$ when the rate of inflation is $3.5\%$, the cost in dollars of Dig-It brand snow shovels is defined by $c\left(t\right)={1.035}^t\left[0.8\sin \left(2\pi t\right)+10.2\right]$ where t is the number of years since January $1,2010$.