5. Suppose that over the time period 1970-1990 the population of Central City at time t is proportional to b^{t} 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 b^{t} 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.