Determine the percentage rate of change of f(x) = $e ^ { 0.9 x }$ at x = 15 and x = 30.
A) $\frac { f ^ { \prime } ( 15 ) } { f ( 15 ) }$ = 22%, $\frac { f ^ { \prime } ( 30 ) } { f ( 30 ) }$ = 5%
B) $\frac { f ^ { \prime } ( 15 ) } { f ( 15 ) }$ = 90%, $\frac { f ^ { \prime } ( 30 ) } { f ( 30 ) }$ = 90%
C) $\frac { f ^ { \prime } ( 15 ) } { f ( 15 ) }$ = 38%, $\frac { f ^ { \prime } ( 30 ) } { f ( 30 ) }$ = 14%
D) $\frac { f ^ { \prime } ( 15 ) } { f ( 15 ) }$ = 17%, $\frac { f ^ { \prime } ( 30 ) } { f ( 30 ) }$ = 29%

Question

Quizplus · Accepted Answer

The derivative of $f(x) = e^{0.9x}$ is $f'(x) = 0.9e^{0.9x}$. The percentage rate of change at any point x is given by $\frac{f'(x)}{f(x)} \times 100\% = \frac{0.9e^{0.9x}}{e^{0.9x}} \times 100\% = 90\%$, which is constant for any value of x, including x = 15 and x = 30.

Determine the Percentage Rate of Change of F(x) = e0.9xe ^ { 0.9 x }e0.9x

Determine the Percentage Rate of Change of F(x) = $e ^ { 0.9 x }$