## Exam-Style Question on Exponential Models## A mathematics exam-style question with a worked solution that can be revealed gradually |

Question id: 434. This question is similar to one that appeared on an IB AI Standard paper (specimen) for 2021. The use of a calculator is allowed.

Doctor Octothorpe investigated the decreasing population of a colony of ants in a remote province of China. His investigation took place in 1958.

He found that during the summer season their population, \(P\), could be modelled by the exponential equation

$$P = 560 + 9560(1.3)^{-t} \quad \text{where} \quad t \ge 0$$where \(t\) is the number of days into the season (\(t = 1\) represents the beginning of 1st June).

(a) Find the population of the ants at the beginning of 31st May 1958.

(b) Find the population of the ants at the beginning of 10th June.

(c) Calculate the date when the population first fell below 1000.

(d) According to this model, find the smallest possible population of ants.

The worked solutions to these exam-style questions are only available to those who have a Transum Subscription. Subscribers can drag down the panel to reveal the solution line by line. This is a very helpful strategy for the student who does not know how to do the question but given a clue, a peep at the beginnings of a method, they may be able to make progress themselves. This could be a great resource for a teacher using a projector or for a parent helping their child work through the solution to this question. The worked solutions also contain screen shots (where needed) of the step by step calculator procedures. A subscription also opens up the answers to all of the other online exercises, puzzles and lesson starters on Transum Mathematics and provides an ad-free browsing experience. |

Drag this panel down to reveal the solution

The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.

The solutions to the questions on this website are only available to those who have a Transum Subscription.

Exam-Style Questions Main Page

To search the **entire Transum website** use the search box in the grey area below.

Do you have any comments about these exam-style questions? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.

©1997 - 2020 Transum Mathematics :: For more exam-style questions and worked solutions go to Transum.org/Maths/Exam/