Question

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?

Answer 1

Answer:

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