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 is a function, P(t) with P measured in rabbits and t measured in weeks.

1. ) Estimate the instantaneous rate of change of P at the instant t=10 weeks

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

Please show all the work so I understand how to do these problems. Thank you

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

Explanation / Answer

at 10 weeks, rate of change = [P(12) - P(10)]/(12 - 10) = (54 - 45)/2 rabbits/week = 4.5 rabbits/week

For a rate of 6 rabbits/week, the change in 2 weeks will be 12 rabbits. This occurs at 14 weeks (between 14-16)

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