Question

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? Drag and drop the choices into the boxes to correctly complete the table. If a value does not match, do not drag it to the table. FunctionWeekly growth rate

Answer 1

The weekly growth rate in this case is 1.6%.

The weekly growth rate, you need to convert the time unit from years to weeks.

There are 52 weeks in a year, so you can use the conversion factor (1 year / 52 weeks).

Rewrite the function in terms of weeks:
`P = 120(1.016)^t * (1 year / 52 weeks).`

Now, you can identify the weekly growth rate, which is the base of the exponential term.

In this case, it's 1.016.

The weekly growth rate is 1.016, and you can express it as a percentage by subtracting 1 and multiplying by 100: Weekly growth rate = (1.016 - 1) * 100%

Weekly growth rate= 1.6%.

Therefore, the weekly growth rate is 1.6%.

Answer 2

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

`P(t)=120(1.016)^t`

If t is the time in years, we have to divide that value by 52 (weeks in the year), then:

`P(t)=120(1.016)^{(t)/(52)}`

What is the weekly growth rate?

The weekly growth rate is:

`(1.016)^{(1)/(52)}=1.0003053`