1 of 8 0-day streak

Logarithmic models in context

Question 1 of 8

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The quantity and its rate are described by this model

The model records the volume recovered from a process over time

L(t)=10 + 12\,\log_e\left(1 + \frac{1}{2}\,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 \(t=2\), the target value is \(L(t)=22\), and the accumulation interval is \([2,4]\)

Determine the value of the model at the start of the interval

(a)1 mark

Determine the value of the model at the start of the interval. The starting time is \(t=0\)

Modelled quantity at the starting time (L)

Format: Give an exact value

(b)1 mark

Evaluate the derivative at the stated time. Use \(t=2\)

Instantaneous rate (L per hour)

Format: Give an exact value

Select the statement that interprets the rate at the stated time. Use \(t=2\)

At \(t=2\), the quantity is decreasing

The modelled quantity at \(t=2\) gives the instantaneous rate, rather than its derivative

The instantaneous rate is measured in hour per L

At \(t=2\), the instantaneous rate is \(3\) L per hour, so the quantity is increasing