What is the rate of change of $f ( t ) = \frac { 2 t - 3 } { t + 5 }$ with respect to t when t = 5?
A) $\frac { 13 } { 100 }$
B) $\frac { 17 } { 10 }$
C) 10
D) $\frac { 7 } { 10 }$

Question

Quizplus · Accepted Answer

The rate of change of a function with respect to a variable is given by its derivative. For $f(t) = \frac{2t - 3}{t + 5}$, we first find its derivative $f'(t)$ using the quotient rule: $f'(t) = \frac{(2)(t + 5) - (2t - 3)(1)}{(t + 5)^2} = \frac{10 + 3}{(t + 5)^2} = \frac{13}{(t + 5)^2}$. Substituting $t = 5$, we get $f'(5) = \frac{13}{(5 + 5)^2} = \frac{13}{100}$.

What Is the Rate of Change Of f(t)=2t−3t+5f ( t ) = \frac { 2 t - 3 } { t + 5 }f(t)=t+52t−3​

What Is the Rate of Change Of $f ( t ) = \frac { 2 t - 3 } { t + 5 }$