Exploring Exponential Growth and Decay in AP Calculus

What does the constant 'c' represent in the exponential growth and decay model?

• The proportionality constant

• The time variable

• The rate of growth or decay

• The initial value

What is the purpose of separating variables in the differential equation?

• To simplify the equation

• To eliminate the constant 'c'

• To find the value of 'k'

• To integrate both sides easily

What mathematical operation is used to solve for 'y' after integrating both sides?

• Division

• Exponentiation

• Multiplication

• Subtraction

How do you find the initial value 'c' in the model?

• By differentiating the equation

• By integrating the equation

• By setting 'y' to zero

• By setting 't' to zero

What is the result of e to the power of zero?

• 0

• 1

• e

• Undefined

How can the initial value 'c' be determined from given conditions?

• By setting 't' to one

• By using the final value of 'y'

• By applying the given initial condition

• By calculating the rate of growth 'k'

What does the constant 'k' represent in the model?

• The rate of change of 'y'

• The proportionality constant

• The time variable

• The initial value

What does the equation 'dy/dt = ky' represent?

• A linear growth model

• An exponential decay model

• An exponential growth model

• A quadratic model

How is the proportionality constant 'k' found in a new scenario?

• By solving an equation involving 'e'

• By using the initial condition

• By differentiating the model

• By setting 'y' to zero

What is the significance of the 'ln' function in finding 'k'?

• It increases the value of 'k'

• It represents natural growth

• It cancels out the 'e' function

• It simplifies the equation