Problema Solution
The value of a particular investment follows a pattern of exponential growth. In the year 2000, you invested money in a money market account. The value of your investment t years after 2000 is given by the exponential growth model A=5200e0.064t. By what percentage is the account increasing each year?
Answer provided by our tutors
A = 52000*e^(0.064*t), e = 2.71828
in 1 year the account will increase by = the difference between (t+1) and t years:
52000*e^(0.064*(t+1)) - 52000*e^(0.064*t) =
= 52000*e^(0.064*t) (e^0.064 - 1)
in percentage it will be
52000*e^(0.064*t) (e^0.064 - 1)/(52000*e^(0.064*t)) =
= e^0.064 - 1 = 0.0661
or in percentage 0.0661*100% = 6.61%
every year the account is increasing by 6.61%.