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3 years ago

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A population of rabbits in a lab, p(x), can be modeled by the function p(x) = 20(1.014)x , where x represents the number of days

since the population was first counted. Explain what 20 and 1.014 represent in the context of the problem [2 points]. Determine, to the nearest tenth, the average rate of change from day 50 to day 100

1 answer:

Nitella [24]3 years ago

7 0

Answer:

20 = initial population of the rabbits

1.014 = growth rate of the rabbits

the average rate of change from day 50 to day 100 is 0.8

Step-by-step explanation:

A population of rabbits in a lab, p(x), can be modeled by the function

p(x) = 20(1.014)^x

This model is exponential. Where 20 = initial population of the rabbits

1.014 = growth rate of the rabbits with 1.4% increase rate of the rabbits

To find the average rate of change from day 50 to day 100,

find the population p(50) and p(100). Subtract them and divide by 100 - 50 = 50.

p(50) = 20(1.014)50 = 40.08...

p(100) = 20(1.014)100 = 80.32...

(80.32 - 40.08) / (100 - 50) = 40.24/50 = 0.8048. which is approximately 0.8 to the nearest tenth.

The rate of change is 0.8.

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