5. Suppose that over the time period 1970-1990 the population of Central City at time t is proportional to bt for some b > 0. If the population of Central City was 36,000 inhabitants in 1970 and 48,000 inhabitants in 1980, what will the population of Central city be in 1990?

 

A. 56,000

B. 58,000

C. 60,000

D. 62,000

E. 64,000

 

 

Solution: The answer is E

 

Let P(t) = Population at any time t. Since P(t) is proportional to bt then,

Let t = 0 for the 1970 population, so that P(0)=36,000. Substitute this result in the above equation and solve for c.

Hence,

Let t = 10 for the 1980 inhabitance of 48,000. Substitute in the above equation and solve for b.

Thus