The sales, s, of a product have declined in recent years. there were 201 million sold in 1984 and 1.3 million sold in 1994. assume the sales are decreasing according to the exponential decay model, upper s left parenthesis t right parenthesis equals upper s 0 e superscript negative kt baseline . 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?

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

For this case we have an equation of the form:

From here, we must find the values of s0 and k.

For this, we use the following data:

There were 201 million sold in 1984 and 1.3 million sold in 1994.

Therefore, the initial sales are:

Then, the value of k is given by:

Clearing k we have:

Thus, the generic equation is:

b) estimate the sales of the product in the year 2002

For the year 2002 we have:

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

By the time 1 single product is sold, we have:

Clearing the time we have:

Therefore, only 1 product will be sold after 38 years.

the answer is b hope you pass

im confused need to go into details plz thx