A town’s census records show a population of 42,500 in the year 2010 and 68,000 in…
MATHEMATICS · Multi-part · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability
Problem
A town’s census records show a population of 42,500 in the year 2010 and 68,000 in the year 2020. Urban planners believe the growth can be described by an exponential function of the form P(t)=Aekt, where t is the number of years after 2010 and P(t) is the population.
(i) Determine the constants A and k using the two census data points.
(ii) Using the model, estimate the population predicted for the year 2025.
(iii) Find the year in which the population is expected to cross one lakh (100,000). Give your answer correct to the nearest year.
(iv) State the domain and range of the function P in this context and justify your choice based on practical considerations.