$139$ Test $3$ Show All the Work to Obtain Full Credit

Name

$[10$ pts$]$ I. Suppose $$1,000$ is invested at an annual interest rate of $6\%.$ Compute the balance after $10$ years if the interest is compounded monthly.

$[10$ pts$]$ II$.$ How long will it take $$5,000$ to grow to $$7,000$ in an investment earning interest at an annual rate of $6\%$ if the interest is compounded continuously.

$[10$pts$]$ III. Find the derivative $f(x)=(xlnx{)}^{\frac{3}{2}}.$

$[10$ pts$]$ IV$.$ Find the equation of the tangent line to the curve $f(x)=x-e^x$ at $x=0.$

$[10$pts$]$ VI$.$ Find the antiderivatives:

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{e}^x\frac{1}{x}dx$