Question

the following rational function models the speed $v(t)$, in miles per hour (mph), of a dragster $t$ seconds since it starts its quarter - mile run. round your answers to 1 decimal place, where necessary.
$v(t)=\frac{370t}{t + 5}$
a. what is the speed of the dragster 8 seconds into its run?
mph
b. write an expression that models the rate at which the speed changes as time changes.
$v(t)=$
c. how fast is the speed changing 8 seconds into the dragsters run? interpret your result.
select an answer
mph.

Explanation:

Step1: Substitute $t = 8$ into $V(t)$

$V(8)=\frac{370\times8}{8 + 5}=\frac{2960}{13}\approx227.7$

Step2: Use quotient - rule to find $V'(t)$

The quotient - rule states that if $y=\frac{u}{v}$, then $y'=\frac{u'v - uv'}{v^{2}}$. Here, $u = 370t$, $u'=370$, $v=t + 5$, $v'=1$. So $V'(t)=\frac{370(t + 5)-370t\times1}{(t + 5)^{2}}=\frac{370t+1850 - 370t}{(t + 5)^{2}}=\frac{1850}{(t + 5)^{2}}$

Step3: Substitute $t = 8$ into $V'(t)$

$V'(8)=\frac{1850}{(8 + 5)^{2}}=\frac{1850}{169}\approx10.9$
The positive value of $V'(8)$ means that the speed of the dragster is increasing 8 seconds into its run.

Answer:

a. $227.7$ mph
b. $V'(t)=\frac{1850}{(t + 5)^{2}}$
c. $10.9$ mph. The speed of the dragster is increasing at a rate of approximately $10.9$ mph per second 8 seconds into its run.