3.7-10 Natural Amd Social Sciences Flashcards
Name sciences and variables that are derivatives.
Velocity
Density
Current
Power
Compressibility
Rate of growth and blood velocity
Marginal cost, marginal profit
Rate of heat flow
Learning curve in psych
Rate of spread of a rumor
What’s the law of natural growth
What’s a differential equation
Involves an unknown function y and it’s derivative
y’ = ky
What are the only solutions to differential equation dy/dt = ky
The exponential functions.
What’s the relative growth rate
Growth rate / population size
What’s equation for compounding interest over n periods of payment
What equation think of when says “grows at rate proportional to its size”?
Y = Ce^kt
Equation for continuous compounding.
Not sure why expression is e
How do you solve related rates problems
Draw diagram
Write equation that relates the rates
Write derivative equation with rates of change by differentiating both sides
Solve for unknown rate
What is the linearization of f at a
Near a on the tangent line
What does C represent in Y = Ce^kt
starting value
what does k represent in Y = Ce^kt
the growth coefficeint.
what do you do if there is a “decay constant” in growth function?
k is negative
If they ask what is the “Decay constant” do you mark as negative or positive?
positive, but it’ll be - k
