A woman invests $5800 in an account that pays 6% interest per year, compounded continuously. a) What is the amount after 2 years? (Round your answer to the nearest cent.)b) How long will it take for the amount to be $8000? (Round your answer to two decimal places.)

Answer:Part a) [tex]\$6,539.48[/tex]  Part b) [tex]5.36\ years[/tex]  Step-by-step explanation:we know that The formula to calculate continuously compounded interest is equal to [tex]A=P(e)^{rt}[/tex]  where  A is the Final Investment Value  P is the Principal amount of money to be invested  r is the rate of interest in decimal  t is Number of Time Periods  e is the mathematical constant number Part a) What is the amount after 2 years? we have  [tex]t=2\ years\\ P=\$5,800\\ r=0.06[/tex]  substitute in the formula above  [tex]A=\$5,800(e)^{0.06*2}=\$6,539.48[/tex]  Part b) How long will it take for the amount to be $8000?we have  [tex]t=?\ years\\ P=\$5,800\\ r=0.06\\A=\$8,000[/tex]  substitute in the formula above  and solve for t[tex]\$8,000=\$5,800(e)^{0.06t}[/tex]  [tex](8,000/5,800)=(e)^{0.06t}[/tex]  Applying ln both sidesRemember thatln(e)=1[tex]ln(8,000/5,800)=0.06t[/tex]  [tex]t=ln(8,000/5,800)/0.06=5.36\ years[/tex]