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10 POINTS Math unit 5.11! PLEASE HELP

The total bear population in a certain area is represented by the function P=120(1.016)t , where t is time in years.

How could this function be rewritten to identify the weekly growth rate of the population? What is the weekly growth rate?

User Madderote
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2 Answers

6 votes

Final answer:

The yearly bear population growth function P = 120(1.016)^t can be rewritten for the weekly growth rate by adjusting the exponent to t/52. The weekly growth rate, calculated as 1.016^(1/52) - 1, is approximately 0.0307% per week.

Step-by-step explanation:

The given function representing the total bear population is P = 120(1.016)^t, where P is the population, 1.016 is the annual growth rate, and t is the time in years. To convert this to a weekly growth rate, we need to account for the number of weeks in a year. Since there are approximately 52 weeks in a year, we would raise 1.016 to the power of 1/52.

Therefore, the function rewritten to reflect the weekly growth rate is P = 120(1.016)^(t/52). To calculate the numeric value of the weekly growth rate, we calculate 1.016^(1/52) - 1, which gives us an approximation of 0.000307 or 0.0307% growth per week.

User Roman Nazarevych
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5 votes

To write the function to show the weekly growth rate of population , we first find the weekly growth rate by dividing yearly growth rate by 52 ( as there are 52 weeks in an year)

Given function is ,


P=120(1.016)^t

or


P=120(1+0.016)^t

To convert in weekly growth rate , divide 0.016 by 52

So formula for weekly growth rate of population is


P=120(1+ (0.016)/(52))^(52t)

or


P=120(1+ (1)/(3250))^(52t)

And the weekly growth rate =
(1)/(3250)

User Rui Wang
by
7.7k points
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