{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

chapter9Problems

# chapter9Problems - Chapter 9 Exponential Growth and Decay...

This preview shows pages 1–3. Sign up to view the full content.

Chapter 9 Exponential Growth and Decay: Differential Equations 9.1 A differential equation is an equation in which some function is related to its own derivative(s). For each of the following functions, calculate the appropriate derivative, and show that the function satisfies the indicated differential equation (a) f ( x ) = 2 e - 3 x , f prime ( x ) = - 3 f ( x ) (b) f ( t ) = Ce kt , f prime ( t ) = kf ( t ) (c) f ( t ) = 1 - e - t , f prime ( t ) = 1 - f ( t ) 9.2 Consider the function y = f ( t ) = Ce kt where C and k are constants. For what value(s) of these constants does this function satisfy the equation (a) dy dt = - 5 y , (b) dy dt = 3 y . [Remark: an equation which involves a function and its derivative is called a differential equa- tion.] 9.3 Find a function that satisfies each of the following differential equations . [Remark: all your answers will be exponential functions, but they may have different dependent and independent variables.] (a) dy dt = - y , v.2005.1 - September 4, 2009 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document