The Function $R ( t ) = 140 + 3 t ^ { 3 }$

Multiple Choice

The function $R ( t ) = 140 + 3 t ^ { 3 }$ represents the value of the U.S. dollar in Indian rupees as a function of time t in days. Find the average rates of change of $R ( t )$ over the time intervals $[ t , t + h ]$ , where t is as indicated and $h = 1$ , $0.1$ , $0.01$ , and $0.0001$ days. Estimate (using $h = 0.0001$ ) the instantaneous rate of change of R at time $t = 7$ . Please select the correct answer rounded to the nearest whole number.

A) 443
B) 441
C) 437
D) 446
E) 444