A-LevelMathematicsLogarithmic and exponential functions9709/31 · Oct/Nov 2017 · Q25 Marks
Two variable quantities x and y are believed to satisfy an equation of the form y = C(aˣ), where C and a are constants. An experiment produced four pairs of values of x and y. The table below gives the corresponding values of x and ln y. X 0.9 1.6 2.4 3.2 ln y 1.7 1.9 2.3 2.6 By plotting ln y against x for these four pairs of values and drawing a suitable straight line, estimate the values of C and a. Give your answers correct to 2 significant figures.
- Two variable quantities x and y are believed to satisfy an equation of the form y = C(aˣ), where C and a are constants. An experiment produced four pairs of values of x and y. The table below gives the corresponding values of x and ln y. X 0.9 1.6 2.4 3.2 ln y 1.7 1.9 2.3 2.6 By plotting ln y against x for these four pairs of values and drawing a suitable straight line, estimate the values of C and a. Give your answers correct to 2 significant figures.[5]
This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.
- [B1] Plot the four points and draw straight line
- [B1] State or imply that In y = ln C + x ln a
- [M1] Carry out a completely correct method for finding In C or In a
- [A1] Obtain answer C = 3.7
- [A1] Obtain answer a = 1.5
Write your answer and get it marked
On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.
Sign up free →