A scientist is observing a population of rabbits in a controlled environment. At

Question

A scientist is observing a population of rabbits in a controlled environment. At the beginning of
the experiment, and then every 2 weeks for 20 weeks, she records the number of rabbits. This data
set is a function, P(t), with P measured in rabbits and t measured in weeks.

P (rabbits) 20 23 27 32 38 45 54 65 78 94 114
t (weeks) 0 2 4 6 8 10 12 14 16 18 20

At what instant in time is the population changing at a rate of 6 rabbits/week?

So by graphing it I know that its going to fall somwhere between 14 and 16 weeks because its increasing at a rate slower than six/week before 14 but faster than six/week after 16. Im not sure how to find the exact week though.

Explanation / Answer

at 14th week rate = .5

at 16th week rate is = 6.5

so the required rate 6 is almost will be at the insathant of 15th week.

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