Rate of change - Applications
Credits to Michael Nolan for orginal work, with answers and additional related resources available on IBEN Exchange.
Covid-19 Daily Infections
1. By adjusting the values for the constants a, b, c, d and k, find an exponential model that approximates the data.
2. Using your model, find the average rate of change of the number of daily infections from 24th to 30th October.
3. By drawing a tangent to your curve, find the instantaneous rate of change of the number of daily infections on 18th October.
Life expectancy in Central African Republic
You can see some data points showing the life expectancy in the Central African Republic from 1960 to 2019. A model has already been produced for this set of data.
1. Using the model, determine when the rate of change of life expectancy is negative. Give your answer to the nearest year.
2. Using the model, determine when the rate of change of life expectancy is positive. Give your answer to the nearest year.
3. In what year is the rate of change of life expectancy the greatest?
4. Using the model, determine when the rate of change of life expectancy stopped decreasing and started increasing. Give your answer to the nearest year.
Rates of change in practical situations
Can you change the vase shape so that the height rises at a constant rate with respect to time? What about a vase shape so that the rate of height of the height chnaging decreases? Can you predict the graph for a variety of differnt common cup and vase shapes?
