Understanding Exponential Change

What is the basic form of a differential equation representing exponential change?

• dy/dt = K * y

• dy/dt = K - y

• dy/dt = y / K

• dy/dt = K + y

When separating variables in the equation dy/dt = K * y, what is the next step after moving dt to the right side?

• Add K to both sides

• Divide both sides by y

• Subtract K from both sides

• Multiply both sides by y

What is the result of integrating dy/y?

• y + C

• 1/y

• ln|y|

• y^2/2

After integrating both sides of the separated equation, what operation is used to solve for y?

• Taking the exponential

• Taking the square root

• Taking the logarithm

• Taking the reciprocal

In the equation y = C * e^(KT), what does the constant C represent?

• The rate of change

• The initial value of y

• The exponential base

• The time variable

Which of the following is a form of the exponential change equation used in chemistry?

• a = a_0 * e^(KT)

• a = a_0 * e^(K/T)

• a = a_0 * e^(T/K)

• a = a_0 * e^(K+T)

What is the equivalent of exponential change in the context of continuous compounding?

• a = P * e^(R+T)

• a = P * e^(T/R)

• a = P * e^(R/T)

• a = P * e^(RT)

What happens when the rate constant K is positive in the exponential change equation?

• The equation becomes quadratic

• The equation becomes linear

• Exponential decay occurs

• Exponential growth occurs

What is the term for exponential growth that approaches a limiting value?

• Logistic growth

• Logarithmic growth

• Quadratic growth

• Linear growth

What is the effect of a negative rate constant K in the exponential change equation?

• It results in exponential growth

• It results in exponential decay

• It results in no change

• It results in linear growth