equations algebra

Question

1. The exponential models below describe the population of the indicated country, A, in millions, t years after 2010.
Russia - A=141.9e^–0.005t
Japan - A=127.3e^–0.006t
Iraq - A=31.5e^0.019t
India - A=1173.1e^0.008t

a. What was the population of Japan in 2010?
b. What was the population of Iraq in 2010?
c. Which country has the greatest growth rate? By what percentage is the population of that country increasing each year?
d. Which countries have a decreasing population? By what percentage is the population of these countries decreasing each year?
e. When will India’s population be 1,377 million?
f. When will India’s population be 1,491 million?

 

Answer 1

a)

 

Evaluate the appropriate function at t=0.  That will be 141.10 million.

 

 

b)

 

Evaluate the appropriate function at t=0.  That would be 127.30 million.

 

 

c)

 

Each country's growth rate is indicated by the coefficient of t.  Therefore, the country who has the highest coefficient of t has the greatest growth rate.  If you want to know the percent each population grows each year, take the coefficient of t and multiply by 100.

 

Iraq and India have an increasing rate because their coefficients of t is positive.

 

 

d)

 

The countries that have a decreasing population are the ones whose module have a negative coefficient of t that is less than 1 but greater than 0.

 

 

e)

 

Solve for t when A=1377 using India's model.  You will need to use logarithms (Ln).  Then,

 

Year = 2010 + t

 

 

f)

 

Do the same as part e).