It is an exponential decline question

Question

The sales, S, of a product have declined in recent years. 1.8 million were sold in 2009 but only 1.2 million sold in 2012. Assume the sales are decreasing according to the exponential model S(t)=Soe^kt

 

A. Find the value of k and write an exponential function that describes the number sold after time, t, in years since 2009. Round to 3 decimal places.

 

b. Estimate the sales of the product in the year 2015. Round to the whoel unit

 

c. In what year will only .8 milliion be sold?

Answer 1

Gwen,

Using the 1.8 million as initial and the 1.2 million as final we have

 

1.2 = 1.8e^3k

<=> 12/18 = e^3k

<=> 2/3 = e^3k

Now take log of both sides

ln(2/3) = ln(e^3k)

<=> ln(2/3) = 3k

=> k = 1/3ln(2/3)

with k known b and c are just a matter of substituting the given values in to the equation

I hope this helps