Question

40 POINTS
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?



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Answer 1

Greetings

Step-by-step explanation:

1.

When trying to find the weekly rate, we need to simply divide the t by 52:

P = $120(1.016)^{\frac{t}{52} }$

2.

To find the weekly growth rate, we need to recall one of the indicies laws:

$a^{bc} = (a^{b})^{c}$

So the $120(1.016)^{\frac{t}{52} }$

Can be rearranged to:

$120(1.016^\frac{1}{52} )^{t}}$

Which gives the result:

120 x ($1.016^\frac{1}{52} = 1.0003$

120(1.0003)$^t$

Or 120( 1 + 0.0003)$^t$

So the weekly growth rate is 0.0003 x 100 = 0.03

So it is 0.03%

Hope this helps!