Mathematical Methods · Unit 1 · Functions and relations · Graphs of relations
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A small business models the relationship between the number of hours worked per week and weekly profit using the relation $P(h) = 15h^2 - 180h + 500$, where $P$ is the profit in dollars and $h$ is the number of hours worked per week. Determine the minimum weekly profit by completing the square. Show all working.
A researcher models the population of a bacterial colony using the relation P(t) = 500e^(0.4t), where P is the population and t is the time in hours after the initial observation. Determine the time required for the population to reach 8000.
A farmer plants a new orchard where the number of fruit trees, $N$, is related to the age of the orchard, $t$ (in years), by the relation $N(t) = 150 - 80e^{-0.3t}$ for $0 \le t \le 20$. Which of the following best describes the behaviour of $N(t)$ as $t$ increases?