The table below shows a persons bank account balance for 5 y

The table below shows a person\'s bank account balance for 5 years. Find an exponential model for this data, with t = 0 corresponding to 1998 Find this person\'s balance in 2010 if it continues to grow at the same rate Estimate the year in which this person\'s account balance will reach S6000

Solution

let exponential function be B(t) = a e^rt

Given that at t = 0 , B(t) = 2000

==> 2000 = ae^r(0)

==> a = 2000

==> B(t) = 2000e^rt

at t = 1 , B(t) = 2130

==> 2130 = 2000e^r(1)

==> e^r = 2130/2000

apply natural logarithms on both sides

==> ln e^r = ln(2130 / 2000)

==> r = ln(2130 / 2000)    since ln a^b = b lna , ln e = 1

==> r = 0.063

Hence B(t) = 2000e^0.063t

b) 2010 ==> t = 12

==> B(12) = 2000e^0.063(12)

==> B(12) = 4259.48

Hence Balance in 2010 is 4259.48

c) B(t) = 6000

==> 6000 = 2000e^0.063t

==> e^0.063t = 3

apply natural logarithms on both sides

==> ln e^0.063t = ln 3

==> 0.063t = ln 3

==> t = (1/0.063) ln 3

==> t = 17.44

Hence in the year 2016 person\'s balance reaches $6000