A biologist is monitoring the population of a specialized algae culture, $P$ (in thousands), in a controlled environment. At time $t$ hours ( $t > 0$ ), the rate of change of the population is modeled by the derivative:

\frac{2t^2 + at + b}{3\sqrt{t}}

where $a$ and $b$ are constants. It is observed that at time $t = 4$ , the population is exactly 10,000 algae ( $P = 10$ ) and the population is growing at a rate of 5,000 algae per hour ( $P^{'} = 5$ ).

Show that $4 a + b = - 2$ .

Given also that $a + b = 7$ ,

Determine, in simplest form, an expression for $P (t)$ .

A researcher adjusts the experiment such that the new population model is given by $G (t) = P (t - 3)$ . Given that the observation at $t = 4$ in the original model is recorded as point $J$ ,

State the coordinates of the corresponding point $K$ on the graph of $G (t)$ .

\frac{2t^2 + at + b}{3\sqrt{t}}

Show that $4 a + b = - 2$ .

Given also that $a + b = 7$ ,

Determine, in simplest form, an expression for $P (t)$ .

A researcher adjusts the experiment such that the new population model is given by $G (t) = P (t - 3)$ . Given that the observation at $t = 4$ in the original model is recorded as point $J$ ,

State the coordinates of the corresponding point $K$ on the graph of $G (t)$ .

1.8 Integration

Question 92

Markscheme

1.8 Integration

Question 92

Markscheme

1.8 Integration

Question 92

1.8 Integration Questions

1.8 Integration

Question 92

1.8 Integration Questions