Question

Total number of DVDs produced in 1998 was0.5 million. in 2004 the total number was 29.01 million. assuming an exponential model applies a) find the value of k and write the function b) estimate # of dvds in 2005,2008, and 2011

Answer 1

x(t) = x0 exp(k*t)
x0 = x(0) = 0.5*10^6
x(6) = x(0) exp(k*6)
x(6)/x(0) = exp(k*6)
k = 1/6*log(x(6)/x(0)) = 1/6*log(29.01/0.5)

For 2005, t = 7
x(7) = x0 exp(k*7)

for 2008, t = 10
x(10) = x0*exp(k*10)

for 2011, t = 13
x(13) = x0*exp(k*13)