Find when the seat is 30 m above the ground for the third time.

Give two reasons why the prediction in part (b)(ii) might be lower than 14.

$c$.

the number of new people infected on day 6.

Use an exponential regression to find the value of $a$ and of $b$, correct to 4 decimal places.

The solution to the differential equation is given by

$Q\left(t\right)=\frac{L}{1+C{\text{e}}^{-kt}}$

where $C$ is a constant.

Using your answer to part (f)(i), estimate the percentage of computers in city X that are expected to have been infected by the virus over a long period of time.

A function $f$ is of the form $f\left(t\right)=p{\text{e}}^{q \cos \left(rt\right)}, p, q, r\in {\mathrm{ℝ}}^{+}$. Part of the graph of $f$ is shown.

The points $\text{A}$ and $\text{B}$ have coordinates $\text{A}(0, 6.5)$ and $\text{B}(5.2, 0.2)$, and lie on $f$.

The point $\text{A}$ is a local maximum and the point $\text{B}$ is a local minimum.

Find the value of $p$, of $q$ and of $r$.

the distance she runs in 20 minutes.

Calculate her distance after 8 minutes. Give your answer in km, correct to 3 decimal places.

For the graph of $f$, write down the period.

the day when the total number of people infected will be greater than 1000.

$L$.

$k$.

Use your answer to part (a) to show that the model predicts 16.7 people will be infected on the first day.

Find the coordinates of A.

How much time is there between the first low tide and the next high tide?

Use the logistic model to find the day when the rate of increase of people infected is greatest.

Perform a ${\chi }^2$ goodness of fit test at the 5% significance level. You should clearly state your hypotheses, the p-value, and your conclusion.

Explain why the number of degrees of freedom is 2.

There are two high tides on 12 December 2017. At what time does the second high tide occur?

Hence predict the total number of people infected by this disease after several months.

Find the value of $p$;

Find the maximum speed of the ball.

Use these parameters to calculate the value of $N\left(8\right)$ predicted by this model.

Determine the rate of change of $h$ when the top of the bucket is at $\text{B}$.

Find $k$.

Hence, write $f\left(x\right)$ in the form $p\text{cos}\left(x+r\right)$.

Find the first time when the ball’s speed is changing at a rate of 2 cm s⁻².

Find the angle through which Mars rotates on its axis each hour.

Find the height of point $\text{A}$ above the ground.

Find $\text{A}\hat{\text{O}}\text{B}$.

Show that $b\approx 0.00939$.

Find the value of $r$.

For the graph of $f$, write down the amplitude.

Find the minimum value of $\omega$.

the minimum value of $R\left(t\right)$.

Find the value of $d$.

her maximum speed, in ms^–1.

Hence show that $a=1.6$, correct to two significant figures.

Hence find the number of rotations the water wheel makes in one hour.

Find the value of $q$;

Calculate the number of seconds it takes for the water wheel to complete one rotation.

Find the difference in height between low tide and high tide.

the maximum value of $R\left(t\right)$.

Show that the maximum value of $\omega =1.98$, correct to three significant figures.

Find the value of $c$.

Write down a sequence of transformations that will transform the graph of $y=\cos x$ onto the graph of $y=f\left(x\right)$.

Assuming a carrying capacity of $5000$ use the given values of $N\left(0\right)$ and $N\left(1\right)$ to calculate the parameters $C$ and $k$.

Comment on the likelihood of the fish population reaching $5000$.