The function $R ( t ) = 42 t - t ^ { 2 }$ 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. Hence, estimate (using $h = 0.0001$ ) the instantaneous rate of change of R at time $t = 7$ . Please round the instantaneous rate to the nearest whole number.
A)29
B) 25
C) 27
D) 28
E) 30

Question

The function $R ( t ) = 42 t - t ^ { 2 }$ 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. Hence, estimate (using $h = 0.0001$ ) the instantaneous rate of change of R at time $t = 7$ . Please round the instantaneous rate to the nearest whole number.  
A)29
B) 25
C) 27
D) 28
E) 30

Quizplus · Accepted Answer

The average rate of change is calculated using the formula $\frac{R(t+h) - R(t)}{h}$. For $t = 7$ and $h = 0.0001$, the instantaneous rate of change is approximately 28.

The Function R(t)=42t−t2R ( t ) = 42 t - t ^ { 2 }R(t)=42t−t2

The Function $R ( t ) = 42 t - t ^ { 2 }$