Date | May 2019 | Marks available | 1 | Reference code | 19M.3.AHL.TZ0.Hca_1 |
Level | Additional Higher Level | Paper | Paper 3 | Time zone | Time zone 0 |
Command term | Show that | Question number | Hca_1 | Adapted from | N/A |
Question
A simple model to predict the population of the world is set up as follows. At time years the population of the world is , which can be assumed to be a continuous variable. The rate of increase of due to births is 0.056 and the rate of decrease of due to deaths is 0.035.
Show that .
Find a prediction for the number of years it will take for the population of the world to double.
Markscheme
* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.
A1
AG
[1 mark]
METHOD 1
attempt to separate variables M1
A1
A1
EITHER
A1
Note: This A1 is independent of the following marks.
OR
A1
Note: This A1 is independent of the following marks.
THEN
(M1)
years A1
Note: If a candidate writes , so then award the final A1.
METHOD 2
attempt to separate variables M1
A1A1
Note: Award A1 for correct integrals and A1 for correct limits seen anywhere. Do not penalize use of in place of .
A1
(M1)
A1
[6 marks]