- YOU DEPOSIT $1,500 
INTO A BANK
THAT PAYS 6% 
CONTINUOUS INTEREST.
WHAT EQUATION CAN BE USED TO 
DETERMINE THE ACCOUNT BALANCE
AFTER 2 YEARS,
WHAT IS THE ACCOUNT BALANCE 
AFTER 5 YEARS,
AND WHEN WILL THE ACCOUNT 
BALANCE REACH $2,500?
SO WE'LL BE USING THE 
CONTINUOUS INTEREST FORMULA
GIVE HERE BELOW.
IT'S ACTUALLY THE SAME FORMULA
THAT WE USED FOR EXPONENTIAL 
GROWTH AND DECAY.
IT'S JUST SOME 
OF THE VARIABLES HAVE CHANGED.
P REPRESENTS THE PRINCIPAL 
OR STARTING AMOUNT,
R IS THE ANNUAL INTEREST RATE 
EXPRESSED AS A DECIMAL,
T IS THE TIME IN YEARS,
AND "A" IS THE AMOUNT 
AFTER 2 YEARS.
SO FOR THIS SITUATION, WE'D 
HAVE THE EQUATION "A" = P,
THE STARTING AMOUNT OF 1,500,
x E RAISED TO THE POWER 
OF R x T.
WELL, THE RATE IS 6%.
6% AS A DECIMAL WOULD BE 
0.06 x T, THE TIME IN YEARS.
SO HERE'S OUR EQUATION
THAT WILL TELL US THE ACCOUNT 
BALANCE AFTER 2 YEARS.
NEXT, WE WANT TO KNOW THE 
ACCOUNT BALANCE AFTER 5 YEARS,
SO WE'LL SUBSTITUTE 5 FOR T.
SO WE CAN SAY "A" OF 5 
IS EQUAL TO 1,500 x E
RAISED TO THE POWER 
OF 0.06 x 5.
AND NOW, WE'LL USE 
THE CALCULATOR
TO GET A DECIMAL APPROXIMATION 
FOR THIS VALUE.
IF WE PRESS 2nd NATURAL LOG,
IT BRINGS UP E 
RAISED TO THE POWER OF,
THEN WE CAN JUST TYPE IN 
0.06 x 5, PRESS ENTER,
AND THE ACCOUNT BALANCE 
IS GOING TO BE APPROXIMATELY
$2,024.79, 
RUN INTO THE NEAREST CENT.
AND THIS LAST QUESTION, 
WE WANT TO KNOW
WHEN THE BALANCE WILL REACH 
$2500 OR $2,500.
SO WE'RE GIVEN "A," WE WANT 
TO SOLVE THE EQUATION FOR T,
SO WE'LL HAVE 
AN EXPONENTIAL EQUATION.
WE NEED TO SOLVE THE EQUATION 
2,500 = 1,500 x E
RAISED TO THE POWER OF 0.06T.
SO WE WANT TO SOLVE 
THIS EQUATION FOR T.
SO WE WANT TO ISOLATE 
THE EXPONENTIAL PART,
SO WE'LL DIVIDE BOTH SIDES 
BY 1,500.
THIS SIMPLIFIES TO 1.
THIS IS ACTUALLY 
A REPEATING DECIMAL,
SO WE'LL LEAVE THIS 
AS A SIMPLIFIED FRACTION.
NOTICE IF WE TAKE 2,500 
DIVIDED BY 1,500.
WE REALLY DON'T WANT 
TO ROUND THIS VALUE.
WE WANT IT TO BE EXACT 
SO OUR IN MORE PRECISE.
SO IF WE PRESS MATH, ENTER, 
ENTER, THIS SIMPLIFIES TO 5/3.
SO WE'LL USE 5/3 HERE
INSTEAD OF A DECIMAL = E 
RAISED TO THE POWER OF 0.06T.
AND NOW TO SOLVE THIS FOR T,
WE'LL TAKE THE NATURAL LOG 
OF BOTH SIDES OF THE EQUATION.
ONCE WE DO THIS,
WE CAN APPLY THE POWER 
PROPERTY OF LOGARITHMS HERE
AND MOVE THIS EXPONENT 
TO THE FRONT.
SO WE'D HAVE NATURAL LOG 5/3 
= 0.06T x NATURAL LOG E.
BUT REMEMBER, NATURAL LOG E 
IS EQUAL TO 1.
MULTIPLYING BY 1 ISN'T GOING 
TO CHANGE ANYTHING.
SO MOST OF THE TIME, 
WE WON'T EVEN WRITE THIS.
SO TO SOLVE THIS FOR T, WE'LL 
DIVIDE BOTH SIDES BY 0.06.
SO ON THE RIGHT SIDE, THIS 
SIMPLIFIES TO 1T OR JUST T.
AND NOW, WE'LL USE 
THE CALCULATOR
TO APPROXIMATE THIS QUOTIENT.
SO WE HAVE NATURAL LOG OF 5/3 
DIVIDED BY 0.06.
SO IF ROUNDED TO THE NEAREST 
10th OF A YEAR,
THIS WOULD BE APPROXIMATELY 
8.5 YEARS.
OKAY, WE'LL TAKE A LOOK 
AT ONE MORE EXAMPLE
IN THE NEXT VIDEO.
