Question 1
2019 SNGS MYA Q7
The concentration of a substance, $P$ (g/dm$^{3}$) in a patient’s blood when the patient consumes a certain diet pill is represented by $P=0.08{{\text{e}}^{kt}}$, where $t$ is the number of hours after the pill has been consumed and $k$ is a constant.
(i)
Find the concentration of the substance before the patient consumes the diet pill.
[1]
When $t=4$, the concentration of the substance is $0.01082$.
(ii)
Find the value of $k$, correct to $1$ decimal place.
[3]
(iii)
Find the time, to the nearest minute, when the concentration of the substance is $0.05$ g/dm$^{3}$.
[3]
(i)
(ii)
(iii)
Question 2
2019 SNGS MYA Q8
(i)
Sketch the graph of $y={{\text{e}}^{3x-1}}$.
[3]
(ii)
In order to solve the equation $3x=1+\ln \left( 2x-1 \right)$, a graph of a suitable straight line is drawn on the same set of axes as the graph of $y={{\text{e}}^{3x-1}}$. Find the equation of this straight line.
[2]
(i)
(ii)
