Solve the Problem $A ( t ) = P e ^ { r t }$

Solve the problem.
-An investment grows exponentially under continuous compounding. After 2 yr, the amount in the account is $6,962.58. After 5 yr, the amount in the account is $8,089.36. Use the model $A ( t ) = P e ^ { r t }$ to
a. Find the interest rate r. Round to the nearest percent.
b. Find the original principal P. Round to the nearest dollar.
c. Determine the amount of time required for the account to reach a value of $17,000. Round to the
Nearest year.

A) $r = 6 \%$ ;
$P = \$ 6,000$ ;
$\mathrm { t } = 17 \mathrm { yr }$

B) $r = 5 \%$ ;
$P = \$ 6,000$ ;
$\mathrm { t } = 21 \mathrm { yr }$

C) $r = 5 \%$ ;
$P = \$ 6,300$ ;
$\mathrm { t } = 20 \mathrm { yr }$

D) $r = 5 \%$ ;
$P = \$ 6,300$ ;
$\mathrm { t } = 19 \mathrm { yr }$