A particular country's exports of goods are increasing exponentially. The value of the exports, t years after 2007 , can be approximated by V (t) equals1.5 e Superscript 0.039 t where tequals0 corresponds to 2007 and V is in billions of dollars. a) Estimate the value of the country's exports in 2007 and 2012. b) What is the doubling time for the value of the country's exports?

V (t) = $ 1.5 billion for 2007

V (t) = $1.5 billion, 295 million. For 2012

Doubling time = t = 177.69 yrs

Explanation:

a).

V (t) = 1.5e^ (0.039t)

For the first year 2007, t = 0

V (t) = 1.5e^ (0.039*0)

V (t). = 1.5e^0

V (t) =. 1.5*1 = 1.5

V (t) = $ 1.5 billion for 2007

For 2012 that is 5 years after, t = 5

V (t) = 1.5e^ (0.0039*5)

V (t) = 1.5e^ (0.0195)

V (t) = 1.5 (1.019691367)

V (t) = 1.5295

V (t) = $1.5 billion, 295 million.

b). Doubling time is when the value of the export is 1.5 * 2 = $ 3 billion

3 = 1.5e^ (0.0039t)

3/1.5 = e^ (0.0039t)

2 = e^0.0039t

In 2 = 0.0039t

0.693 = 0.0039t

t = 177.69 yrs