Initial Knowledge Check

$100$ points possible Answered: $\frac{2}{16}$

Progress savee

$6$ pts

$1$

Details

Ecologists estimate that, when the population of a certain city is $x$ thousand persons, the average level Lof carbon monoxide in the air above the city will be L ppm $($parts per million$),$ where $L(x)=800\mathrm{.}4x0\mathrm{.}0002x^2.$

The population of the city is estimated to be $x(t)=75015t0\mathrm{.}5t^2$ thousand persons tyears from the present.

a$)$ What is the rate of change of garbon monoxide with respect to the population of the city?

$\frac{dL}{dx}=$

$$

b$)$ What is the rate of change of thetpopulation with respect to time?

$\frac{dx}{dt}=$

$$

c$)$ What is the rate of change of carbon monoxide with respect to time?

$\frac{dL}{dt}=$

$$

d$)4$ years from now, the population of the city will be $$ thousand persons.

e$)4$ years from now, the population will be increasing at the rate of $$ thousand persofts per year.

f$)4$ years from now, the level of carbon monoxide will be rising at the rate of

$do\frac{m}{v}$ear. $($round to $1$ decimal place$)$