The sales S of a product have declined in recent years There

The sales, S, of a product have declined in recent years. There were 202 million sold in 1984 and 1.4 million sold in 1994. Assume the sales are decreasing according to the exponential decay model, S(t)=S₀e^-kt

a) Find the value k and write an exponential function that describes the number sold after time, t, in years since 1984.

b) Estimate the sales of the product in the year 2002.

c) In what year (theoretically) will only 1 of the product be sold?

Solution

S(t) = Soe^-kt

Let t=0 in 1984 ( 0, 202 miil)

1994 : ( 10, 1.4miilion)

So, 1.4 = 202e^-10k

1.4/202 = e^-10k

Take natural log on both sides:

4.97 = 10k

k = 0.497

S(t) = 202e^-0.497t

b) in 2002 : x = 18

S(t) = 202e^-(0.497*18) = 2.7563742e-37 million   .It negligibel value

There something wrong with the value : in 1984 202 million sold.

As 202 million in 1984 and just 1.4 million in 1994

The method of solution remains same