Interactive practice questions
In a closed habitat, the population of kangaroos $P\left(t\right)$P(t) is known to increase according to the function $P'\left(t\right)=\frac{t}{4}+6$P′(t)=t4+6, where $t$t is measured in months since counting began.
Determine the total change in the population of kangaroos in the first $8$8 months since counting began.
Solve for $T$T, the number of months it will take from when counting began for the population of kangaroos to increase by $128$128.
The population growth rate of rabbits is given by $p\left(x\right)$p(x), as shown in the graph below.
The total population growth of rabbits over $n$n years is given by $\int_0^np\left(x\right)dx$∫n0p(x)dx as shown in the table below.
An object is cooling and its rate of change of temperature, after $t$t minutes, is given by $T'=-20e^{-\frac{t}{3}}$T′=−20e−t3.
Calculate the average rate of change $f\left(x\right)$f(x) if $f'\left(x\right)=6\sin3x$f′(x)=6sin3x over the domain $\frac{\pi}{6}\le x\le\frac{\pi}{3}$π6≤x≤π3.