1 of 8 0-day streak

Logarithmic models in context

Question 1 of 8

Calculator allowed

Use the model and the units stated below

The volume of water recovered by a filter is modelled after the process begins

S(t)=12 + 15\,\log_e\left(1 + \frac{1}{3}\,t\right)

The model is used for \(0\le t\le 6\). The time \(t\) is measured in hours, and the quantity is measured in L

The rate is evaluated at \(t=4\), the target value is \(S(t)=27\), and the accumulation interval is \([0,1]\)

Find the modelled quantity at the starting time

(a)1 mark

Find the modelled quantity at the starting time. The starting time is \(t=0\)

Modelled quantity at the starting time (L)

Format: Give an exact value

(b)1 mark

Calculate the rate of change at the given time. Use \(t=4\)

Instantaneous rate (L per hour)

Format: Give an exact value

Choose the correct direction and units for the instantaneous rate. Use \(t=4\)

At \(t=4\), the instantaneous rate is \(\frac{15}{7}\) L per hour, so the quantity is increasing

At \(t=4\), the quantity is decreasing

The instantaneous rate is measured in hour per L

The modelled quantity at \(t=4\) gives the instantaneous rate, rather than its derivative