$[0/10$ Points$]$

Alice invests $$2000$ at Bob's bank and $$4000$ at Charlie's bank.

Bob's bank compounds interest continuously at a nominal rate of $7\%.$

Charlie compounds interest continuously at a nominal rate of $3\%.$

Answer the following:

$($a$)$ In how many years will the two investments be worth the same amount?

Give an exact answer! Decimal approximations may be marked as incorrect.

Answer:

$($b$)$ What is that common amount when the two accounts have the same value?

Note: Give an exact answer, or an answer correct to the nearest cent.

Answer: $

$[5/10$ Points$]$

Alice makes an initial investment on September $1,2000$ into a bank account on that compounds continuously at an unknown rate.

On September $1,2002,$ the balance was $$230\mathrm{.}00.$ On September $1,2014,$ the balance was $$440\mathrm{.}00.$ Answer the following.

$($a$)$ Determine the interest rate. Your answer must be exact, that is$,$ symbolic $($NO decimal places anywhere$).$

Interest Rate $=,\%($no decimals! Your answer is a Percentage.$)$

$($b$)$ Determine the initial investment. Your answer must be correct to the nearest cent. $($Use the exact answer from part $($a$)$ to insure your answer is accurate.$)$

Initial Balance $=$$