According to a joint study conducted by$$Oxnard$\text{'}$s$$Environmental Management and a state government agency, the concentration of carbon monoxide $($CO$)$ in the air due$$to automobile exhaust$$t$$years from now is given by$$C$($t$)=0\mathrm{.}01(0\mathrm{.}2$t$^2+4$t$+64)^(2/3)$in parts per million.$$ To find the rate at which the level of CO is changing with respect to time, we compute the derivative$$dC$/$dt$$or$$C $\text{'}($t$).$

Suppose the derivative can be simplified to approximately$$C $\text{'}($t$)=[0\mathrm{.}00456*($t$+10)]/[($t$^2+20$t$+320)^(1/3)].$ Then,$$C $\text{'}(1)$represents the rate$$at which the level of CO is changing $1$ year from now, which is approximately $0\mathrm{.}0072$ parts per million per year.$$

What is$$the rate$$at which the level of CO is changing$4$ years from now?

Group of answer choices

$0\mathrm{.}0081$ parts per million per year

$0\mathrm{.}0090$ parts per million per year

$0\mathrm{.}0086$ parts per million per year

$0\mathrm{.}0077$ parts per million per year

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