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

= PMT(B8/12,B10,B5)

Explanation:

The excel PMT function is calculated using the following formula

PMT(rate, nper, pv, [fv], [type])

Where rate = rate of payments per month

nper = duration of payment in month

pv = Present Value

fv = future value (it's an optional field)

type = payment type (it's an optional field)

Given that

B8 = rate

B10 = nper

B5 = pv

In cell B12, type the following

= PMT(B8/12,B10,B5)

We're making use of B8/12 because we need the rate to be in months not years.

Since there are 12 months in a year, monthly rate = B8/12

To use this formula in C12:D12

Use the following;

In cell C12, type the following

= PMT(C8/12,C10,C5)

In cell D12, type the following

= PMT(D8/12,D10,D5)