The value of k such the the solution ofdifferential equationof dx/dt = kx is k = ln(3).What is differential rule of exponential function?By multiplying the originalexponential functionby the derivative of its power, one can differentiate an exponential.The rule for differentiating an exponential function is  f(x)=a^u = a^t ln(t).The given function is:x(t) = 3^tUsing the differential rule for the exponential function we have:d/ dt (3^t) = 3^t ln(3)Substituting the value of x(t) in the equation with 3^t ln(3) we have:3^t ln(3) = k 3^tSince 3^t is a non-zero expression the value of k corresponding to the given value is:ln(3) = kHence, the value of k such the the solution of differential equation of dx/dt = kx is k = ln(3).Learn more aboutdifferential equationhere:brainly.com/question/14620493#SPJ4...

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