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Math - Discrete or Continuous function?
Determine the kind of function, discrete or continuous?
i) The population of a city increases yearly at rate of 3.5%. The pop. modeled with the equation n(t) = 75,260(1.035)^t, as t is time in years from 2001. Determine the pop. in 2019.
ii) The life in a battery decreases 0.25% every 6 hrs. It is modeled by the function c(h) = 100(0.9975)^h/6, as C is level of charge as percent. What is percentage of the battery after 25 days?
4 Answers
- Anonymous8 years agoFavorite Answer
both of equations are continuous, as you obtain values that can be any real number between 0 and infinity in (i), and anything between 100 and 0 in (ii)
I'm not 100% sure about part (i) though, because even though the model equation for the population is continuous, the actual thing you're estimating is a discrete thing.. the number of people in a city is finite, its discrete, you can't have 4.83756377.... number of people. So its a bit of an ambiguous question. If you are calling n(t) the function, then yes its continuous, but if the function is the estimate for the population, then you could say its discrete.
- 8 years ago
Not sure if i) would be a continuous function as it is simply not possible to get half a person of a population. The second one would definitely be continuous.
- 8 years ago
Both are continuous. You can plug in a decimal input and still get a sensible answer.
