Please work problem # 38 in Test 2, Section 4.

This one is all about following the formula and knowing where to plug the given numbers in. Here’s the formula:

N_{\text{next year}}=N_{\text{this year}}+0.2\left(N_{\text{this year}}\right)\left(1-\dfrac{N_{\text{this year}}}{K}\right)

The N values are obvious: they represent the number of plants the botanist will have this year and next year. K is less obvious from the formula, but the description of the formula tells you what it is: K is the number of plants the environment can support. That, it turns out, is what question #38 is asking you to solve for. To go from 3000 plants this year to 3360 next year, what must the value of K be?

3360=3000+0.2\left(3000\right)\left(1-\dfrac{3000}{K}\right)

3360=3000+600\left(1-\dfrac{3000}{K}\right)

360=600\left(1-\dfrac{3000}{K}\right)

\dfrac{360}{600}=1-\dfrac{3000}{K}

0.6=1-\dfrac{3000}{K}

-0.4=-\dfrac{3000}{K}

-0.4K=-3000

K=\dfrac{3000}{0.4}

K=7500

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