The equation ( mathrm{A}( mathrm{t})=5000 e^{0.041} ) gives the balance after ( t ) years of an initial investment of 5000 dollars which pays ( 4.00 % ) compounded continuously. a. Find a formula for ( frac{d A}{d t} ) b. Find and interpret ( A^{ prime}(11) ). Include appropriate units. c. Compare the approximation of ( $ 311 ) to

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The equation  (  mathrm{A}( mathrm{t})=5000 e^{0.041}  ) gives the balance after  ( t  ) years of an initial investment of 5000 dollars which pays  ( 4.00  %  ) compounded continuously. a. Find a formula for  (  frac{d A}{d t}  ) b. Find and interpret  ( A^{ prime}(11)  ). Include appropriate units. c. Compare the approximation of  (  $ 311  ) to the actual change. Report your answer to two decimal places.

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