The function $R ( t ) = 1,120 + 79 t - t ^ { 3 }$ represents the value of the U.S. dollar in Indian rupees as a function of the 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. Hence, estimate (using $h = 0.0001$ ) the instantaneous rate of change of $\text { R }$ at time $t = 2$ .
Select your answer rounded to the nearest whole number.

A)63
B) 69
C) 64
D) 67
E) 68

Question

The function $R ( t ) = 1,120 + 79 t - t ^ { 3 }$ represents the value of the U.S. dollar in Indian rupees as a function of the 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. Hence, estimate (using $h = 0.0001$ ) the instantaneous rate of change of $\text { R }$ at time $t = 2$ .  
Select your answer rounded to the nearest whole number.
 
A)63
B) 69
C) 64
D) 67
E) 68

Quizplus · Accepted Answer

The average rate of change is calculated using the formula $\frac{R(t+h) - R(t)}{h}$. For $t = 2$ and $h = 0.0001$, the calculation gives approximately 67.

The Function R(t)=1,120+79t−t3R ( t ) = 1,120 + 79 t - t ^ { 3 }R(t)=1,120+79t−t3

The Function $R ( t ) = 1,120 + 79 t - t ^ { 3 }$