Question

Compute (accurate to at least 8 decimal places) the average rate of change of the population of fish between $t=5$ and the following values of $t$=5.5

The population (in hundreds) of fish in a pond is given by $P\left(t\right)=2t+\sin \left(2t-10\right)$

Answer 1

$P\left(t\right)=2t+\sin \left(2t-10\right)$

$Substitute\; 5\; for\; t.$

$P(5)=2\mathrm{(5)}+\sin \left(\mathrm{2(5)}-10\right)$

$=10+sin(0)$

$=10$

$Substitute\; 5.5\; for\; t.$

$P(5.5)=2\mathrm{(5.5)}+\sin \left(\mathrm{2(5.5)}-10\right)$

$=11+sin(1*180/\pi )$

$=11.84$

$----------------$

$Calculate\; the\; average\; rate\; of\; change,$

$ARC\; =(P(5.5)-P(5))/(5.5-5)$

$=(11.84-10)/(0.5)$

$=3.68$