Question

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?

Answer 1

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.

Answer 2

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)`