In Problems 1–8, express the relationship between f′ ( x ) and f ( x ) in words, and write a differential equation that f ( x ) satisfies. For example, the derivative of f ( x ) = e 3 x is 3 times f ( x ); y ′ = 3y. ( If necessary, review Section 3.4 ). 5. f ( x ) = 3.2 e x 2
In Problems 1–8, express the relationship between f′ ( x ) and f ( x ) in words, and write a differential equation that f ( x ) satisfies. For example, the derivative of f ( x ) = e 3 x is 3 times f ( x ); y ′ = 3y. ( If necessary, review Section 3.4 ). 5. f ( x ) = 3.2 e x 2
Solution Summary: The author explains that the relationship between fprime '(x)' and
In Problems 1–8, express the relationship between f′(x) and f(x) in words, and write a differential equation that f(x) satisfies. For example, the derivative of f(x) = e3xis 3 times f(x);y′ = 3y. (If necessary, review Section 3.4).
8) Determine the equation of an exponential function of the form y = a · b* that contains the points
(4,-486) and (5, -1458).
Does y =e9-x2-2 exist?
Model the following data using an exponential function of the
form f(x) = Ab". You need to do this rigorously, that is, set up a system of
equations, and solve it to get A and b. Getting the right answer by guessing
will earn no credit.
(a) f(x) is exponential and goes through the points (1, 2) and (4,6).
(b) f(x) is exponential and goes through the points (2, 75) and (5, 9375).
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Fundamentals of Differential Equations and Boundary Value Problems
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