A researcher believes that if x thousand individuals among a susceptible population are inoculated (made no longer susceptible to a disease), then a function of form I(x)=a⋅R^x−b for constants a, b, and R would model the eventual number of infected individuals (also in thousands). Let R=0.9 (a) If the susceptible population is 5000 and no one is inoculated, how many will eventually be sick? . What point does that imply should be on the graph of the function I(x)? ( , ) (b) If the susceptible population is 5000 and everyone is inoculated, how many will eventually be sick? . What point does that imply should be on the graph of the function I(x)? ( , ) (c) Use the results of parts (a) and (b) to find approximate values for the constants a= ( ) and b= ( ) in the researcherâs model. (d) According to the model, how many susceptible individuals will be infected if half of them are inoculated?
Rate of Change
The relation between two quantities which displays how much greater one quantity is than another is called ratio.
Slope
The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:
A researcher believes that if x thousand individuals among a susceptible population are inoculated (made no longer susceptible to a disease), then a function of form
for constants a, b, and R would model the eventual number of infected individuals (also in thousands). Let R=0.9
(a) If the susceptible population is 5000 and no one is inoculated, how many will eventually be sick? . What point does that imply should be on the graph of the function I(x)? ( , )
(b) If the susceptible population is 5000 and everyone is inoculated, how many will eventually be sick? . What point does that imply should be on the graph of the function I(x)? ( , )
(c) Use the results of parts (a) and (b) to find approximate values for the constants
a= ( )
and b= ( ) in the researcherâs model.
(d) According to the model, how many susceptible individuals will be infected if half of them are inoculated?
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