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 eat. 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,