6. A population grows exponentially. At 10 years, the population is 1,000. At 20 years, it is 2,000. What was the approximate population at 5 years?
A. 140 |
B. 250 |
C. 500 |
D. 700 |
E. 750 |
Solution: The answer is D
Let P(t) = the population at any time t. To say that the population grows exponentially is the same as saying that the population is directly proportional to e^{at}. So, we have the following equation,
Since, P(10) = 1000 and P(20) = 2000 we can solve for k and a as follows,
Thus,
So, the approximate population at 5 years is given by,